Bilbao improved in the second period and had one back through Mikel Rico just before the hour. Minutes later, Barca had their third, however, when Oscar de Marcos turned in a goal-bound effort from Messi.
Barca then had a fourth when Neymar converted from inside the box, but Bilbao quickly responded through Aritz Aduriz for 4-2.
The hosts were reduced to 10 men for the final 15 minutes, meanwhile, after Xabier Etxeita was sent off for a poor challenge on Suarez. The suffering was not over, however, with Pedro adding a fifth for Barca late on.
Read how it all unfolded in Sports Mole's minute-by-minute live commentary of the action below.
Evening all! Sports Mole's live La Liga coverage continues from San Mames as Athletic Bilbao welcome Barcelona. Bilbao managed to end their seven-game winless run last time out at Levante, but Barca will enter this match off the back of eight successive victories in all competitions. That said, Bilbao did record a 1-0 win when these two sides met at San Mames in the league last season.
As it stands, Bilbao sit 13th in the table on 23 points. They have won just six of their 21 league games, drawing five and losing 10. Their home form has been a bit of a disappointment, with just three victories from their 10 league games at San Mames – scoring just 11 times in the process. They finished fourth last season, but a Champions League position is a long way off at this stage of the season.
Barca, meanwhile, remain second in the table on 50 points following Atletico Madrid's 4-0 win over Real Madrid on Saturday. They are now just four points off the pace and victory here would put them on Real Madrid's coat-tails. It is an excellent chance to close the gap on first spot to just one point.
Here we go then. Both sets of players join us on the pitch for the first period. It must be said that there is a wonderful atmosphere inside the ground as the home side get the first 45 minutes underway.
As expected, it has been a fast start from the home side, with Muniain taking the ball away from Mathieu deep in the Barcelona half. This really is a classic La Liga affair. Goals please!
Barcelona have just started to enjoy possession in the last couple of minutes, but a period of pressure comes to a close when Messi is challenged by Rico. Bilbao will have to spend long periods without the ball this evening, while patience will be key for the visitors. It should be a fascinating battle.
Neymar has his dancing shoes on this evening there is no doubt about that, with the Brazilian already causing problems in a wide area. Not too much from Bilbao thus far, but Aduriz has attempted to turn Mathieu on a couple of occasions. The Frenchman will surely be targeted by Bilbao this evening.
Barcelona are asking questions of the referee each time a challenge is made, which is not going down too well with the home supporters. Bilbao have a half-chance as Aduriz meets a corner from the right, but the striker clips his effort high of the crossbar. Bright opening eight minutes here.
Possession football from Barca in the last couple of minutes, but Bilbao are putting pressure on the visitors in the final third. Suarez attempts to run away from the Bilbao defence, but the striker is penalised for handball. Still goalless, but there are signs that we will have goals at San Mames.
Suarez attempts to fashion a shooting chance after collecting a pass from Alba, but Laporte is on hand to make the clearance. The pressure continues from Barca, however, as they pass and probe.
Suarez has had some rough treatment in the opening 14 minutes, with both Bilbao centre-backs closely marking the forward. Barca have a half-chance as Messi threatens to drive into the box, but Rico is across to make the clearance. Really important period of the match as Barca turn the screw.
Who else? Barca open the scoring with 15 minutes on the clock as Messi's deflected free kick finds its way into the back of the net. Iraizoz appeared to be dealing with the strike, but it took a wicked touch off a Bilbao shirt, before ending up in the bottom corner. Advantage Barca at San Mames!
Aduriz leads the response team for Bilbao, but the striker's effort was always moving high and wide of the crossbar. It is vital that the home side score the next goal in this match. Absolutely vital.
... CHANCE! Bilbao have a stunning chance to level as Muniain delivers a super cross towards Aduriz, who makes contact, but Bravo is on hand to make the save. The opportunity came in the second phase of the initial free kick. This is hotting up nicely with 20 minutes on the clock.
SAVE! Save of the season from Iraizoz. Just stunning from the Bilbao goalkeeper as he somehow keeps out Suarez after the striker had met a cross from Messi. It was a bullet header from the Barcelona forward, but the goalkeeper somehow tupped it over the crossbar. Good grief!
Another half-chance for the away side as Neymar finds the head of Xavi, but his header is high of the crossbar. Barca could be out of sight after just 23 minutes. They are in complete control now.
Too good from Barca, just too good. Finally Suarez breaks his duck as the striker rattles one into the bottom corner following excellent work from Messi. Game over? Quite probably to be honest.
Good pressure from Bilbao in the last couple of moments, but they are obviously worried about the counter-attacking threat from Barca, who have been stunning in the opening 29 minutes here.
OFF-THE-LINE! Barca come close to scoring a third as Xavi rounds the Bilbao goalkeeper before setting up Neymar, but his effort is cleared off the line by Laporte. Excellent defending from the centre-back. Barca could seriously be four or five goals ahead at the moment.
POST! Bilbao come close to opening their tally for the evening as Aduriz meets a poor header from Pique, but his own header smashes the post. Poor defending from Barca there!
Bilbao just have to score the next goal here. The home side want a penalty as Busquets appears to pull Laporte to the ground inside the box, but the referee is not interested. Better from Bilbao.
Neymar has had some rough treatment in the first period and that continues as De Marcos flies into the back of the Brazilian. Barca are in the mood for more goals as they continue to press forward.
It is all very comfortable for Barca at the moment as they continue to force the issue. Xavi attempts to slide a pass into Neymar, but it is just too strong for the Brazilian. The home supporters remain in good voice with little over five minutes of the first period remaining. Bilbao MUST score next.
Half-chance for Suarez as the Barca forward meets a deep cross from Alves, but his effort was wide of the post. De Marcos just prevented the Uruguay international from making clear contact.
Bilbao simply cannot afford to concede a third before the break or it really would be game over. The visitors continue to pass and probe, with the home team being moved all over the pitch.
CHANCE! Excellent chance for Barca to score their third as Messi slots a wonderful pass into Neymar, but the Brazilian is denied by an excellent last-ditch challenge from Laporte.
So there we have it. The referee brings the first period to a close, with Barcelona leading 2-0 courtesy of goals from Messi and Suarez. Bilbao have had their moments, with Aduriz hitting a post, but it has been a match dominated by the visitors, who are heading for a ninth straight win in all comps.
STATS! Barca have dominated the possession with 70%, while they have had eight attempts - five of which have been on target. Bilbao, meanwhile, have hit the target with two of their six attempts. There has also been two yellow cards, with Balenziaga and Alves both in the book.
BENCH WATCH! Bilbao boss Valverde might look to his bench sooner rather than later and the Spaniard has the likes of Benat, Ibai Gomez and Inaki Williams in reserve. Barcelona, meanwhile, have options in the shape of Iniesta, Pedro and Rafinha - it really is some bench for the visitors.
Here we go then. Both sets of players join us on the pitch for the second period. Can Bilbao find some way of getting back into this match? Barca get the second 45 minutes underway at San Mames.
No changes from either manager at the interval, which is not all that surprising. However, I suspect that alterations will occur if the score remains 2-0 Barca for the next 20 minutes or so.
Not much of an atmosphere inside the stadium at the moment. Bilbao really need a goal to lift the volume inside the ground. Barca are comfortable at this stage and that will remain the case unless the hosts can find some sort of inspiration. Inaki Williams from the bench will be a consideration.
Half-chance for Neymar following some lacklustre defending from the home side, but Laporte manages to carry the ball away at the vital moment. Another goal for Barca would certainly end this contest.
CHANCE! Barcelona come close to scoring their third as Suarez rolls a low cross towards Messi, but Aurtenetxe manages to shoulder the Argentine out of the way. Excellent defending!
CHANCE! Wonderful chance for the home side this time as Unai Lopez meets a super cross from De Marcos, but his effort is wide of the post. The Spaniard just had to score there!
Another half-chance for the home side as Muniain slides an excellent pass into Aduriz, who spins inside the box, but Pique is on hand to block the striker's effort. Barca are down the other end moments later, but Suarez's effort is deflected wide of the post. End-to-end football at San Mames!
Little over 30 minutes of football remaining and Barca still lead 2-0 at San Mames. Bilbao are now pressing, however, which is raising the atmosphere inside the stadium. Good game now!
Lifeline Bilbao! The hosts open their tally for the evening as Rico smashes home from close range after Bravo had denied an excellent strike from Aduriz. Game on at San Mames that is for certain!
CHANCE! Messi is straight down the other end and almost sends Barca 3-1 ahead, but the Argentine's effort hits the side netting. End-to-end football with around 30 minutes remaining.
Messi has his second off the evening as the Argentine bundles home following an excellent cross from Suarez. It might just go down as an own goal from De Marcos, who certainly made contact.
Well, this match has just burst into life now! Bilbao are not finished as Lopez strikes one from outside the box, but Bravo is on hand to make the save. End-to-end football at the moment.
Game over then! Barca have their fourth as Messi sets up Neymar, who slides a low effort into the bottom corner. Excellent finish from the Brazilian and there is surely no way back for Bilbao.
CHANCE! Barca have the chance to score a fifth as Neymar meets a through pass from Suarez, but the Brazilian is denied by Iraizoz. Barca are running absolute riot at the moment.
It is raining goals! Bilbao have their second as Aduriz collects a smart pass from Muniain before finishing from a tight angle. This match was 2-0 a little while ago! What on earth!
Little under 20 minutes of football remaining and Barca lead 4-2 in what has been an incredible match. Neither side is finished attacking, however, as both continue to commit numbers in the final third.
Possession football from Barca in the last couple of minutes, which is not much of a surprise. Rafinha is preparing to enter proceedings for the visitors and that will occur in the next break.
CHANCE! Suarez comes close to scoring his second as Adriano floats an excellent cross onto the head of the forward, but his effort was always moving wide of the post.
RED CARD! Etxeita (Bilbao): The home side are reduced to 10 men as Etxeita flies into a high challenge with Suarez. Terrible from the defender and that is a correct decision.
Possession football from the away side in the last couple of minutes, which is not much of a surprise. They are in control and as it stands, will move one point behind the league leaders Real Madrid.
It is almost like a training exercise for the away side at the moment, with Bilbao prepared to sit deep and accept the defeat as it stands. Little over five minutes of normal time remaining here.
Barca have a fifth goal as Pedro turns a low Busquets cross into the back of the net following excellent work from Messi. Too good from the Catalan side this evening. Just too good.
Not many teams come to Bilbao and score five goals, but Barca are in sensational form at the moment. Bilbao's suffering is almost over as we approach the final minute of normal time here.
Neymar has the chance to score a sixth for the away side, but the Brazilian's long-range effort is straight into the arms of the goalkeeper. The home supporters are in fine voice here!
So there we have it. The referee brings the second period to a close with Barca running out 5-2 winners. Thanks for joining Sports Mole for the action. Good evening!
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