Blackpool boss Neil Critchley praised his Championship newcomers for never giving up after Shayne Lavery's stoppage time strike had earned a battling point at Ashton Gate.
The newly-promoted visitors looked to be heading for certain defeat until Lavery got on the end of a low cross from fellow substitute Josh Bowler to fire past Dan Bentley from close range.
The goal was a sickener for City boss Nigel Pearson, who appeared to be on course for his first home win since taking charge when Chris Martin headed in Andy King's 44th-minute cross.
The Robins have not won at Ashton Gate since January, but that did not worry Critchley or the 1,100 travelling Blackpool fans, who ended the game with wild scenes of celebration.
Critchley said: "It feels like a win and to see our supporters celebrating at the end was very humbling.
"From the start of my time in charge, I wanted the team to reflect the people who live in our area.
"That meant fighting to the last. We did that today and after an improved second-half performance we got our reward.
"Bristol got on top of us in the first half and we lacked a bit of confidence and belief in ourselves.
"In the end, we were a match for them, which is very encouraging. They will expect to do well this season.
"We learned what we knew already, that the Championship is a very tough league. It may only be a point, but to get it like that will give everyone a lift.
"We are the bookmakers' favourites to go down, which was no surprise. But I have faith in the players and expect us to be competitive in a very tough league.
"Our fans love to party and it's nice to have given them reason for that today. But games come thick and fast and there is no room doing anything but look ahead to the next one."
City had created virtually all the clear chances in front of an 18,000 crowd before Lavery's late strike and Pearson was understandably frustrated.
He said: "Everything was pretty positive up to that last moment when we could have done a lot more to prevent the goal.
"I feel like everyone associated with the club probably feels. It was a game we should have won and to concede so close to the end was very disappointing.
"There was a lot we might have done to prevent the goal. But I am not going to spend a lot of time picking the bones out of it.
"The overall performance was good, but it was a reminder of what football can do to you at times.
"I thought we looked fitter and sharper than last season and the new signings fitted in well.
"We probably should have been more than one goal up and need to make it count more when we are on top.
"But I have a talented group of players and enough of them are now fit for us to name a very different team in the cup against Forest Green in midweek.
"The Championship is the priority, but we have sufficient talent to do well in other competitions as well."
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