Mads Bech Sorensen's second-half equaliser at Huddersfield moved Brentford up to third in the Championship table but Thomas Frank's men sit nine points adrift of the top two.
A run of one win from their last six away contests has undermined the Bees' automatic promotion hopes and the visitors had to come behind in this encounter after gifting Lewis O'Brien an early goal in West Yorkshire.
The Terriers midfielder capitalised fully on a dismal defensive mix-up to open the scoring after only seven minutes when keeper David Raya rushed out of his goal to the edge of the box to deal with a long ball forward but right-back Mads Roerslev elected to play a short pass inside instead.
That was swiftly intercepted by the alert Alex Vallejo and O'Brien was then just as decisive as he directed a low 20-yard shot past the out-of-position Raya in what proved to be the only goal attempt of the first half for Carlos Corberan's men.
At the other end, Christian Norgaard's header from a right-wing Sorensen cross was comfortably caught by Ryan Schofield, while Naby Sarr made an excellent sliding block to repel Vitaly Janelt's goalbound drive after Sergi Canos' clever ball through the left channel.
Sarr went on to survive strong penalty appeals for handball, while Norgaard cleared the crossbar from the edge of the penalty box after Sorensen had attacked the byline.
Moments later, Bryan Mbeumo also aimed too high from a similar distance for the Bees and the same player was inches away from meeting a headed flick-on by Ivan Toney after flinging himself forward at the far post.
Mbeumo also swung his leg at a Norgaard cross in the final act of the first half but failed to make meaningful contact.
Frank's side were back on level terms, however, five minutes into the second period.
Sarr again performed heroics to clear Pontus Jansson's header off the line but Janelt quickly retrieved the loose ball and squared for Sorensen to stab in from seven yards.
Within a minute, the visitors might have gone ahead when Toney beat Schofield with a diagonal shot across the face of goal but his effort thumped against the Huddersfield keeper's left-hand upright.
That sparked a little attacking life into the hosts with Juninho Bacuna curling over from a free-kick and O'Brien tangling with Saman Ghoddos in the box, but his shouts for a spot-kick fell on deaf ears.
In between, Ghoddos had seen a 20-yard chest-and-volley attempt bounce wide, while Mbeumo went on to miss the target with headers from Sorensen and Roerslev deliveries.
At the other end, Demeaco Duhaney broke through the right channel and cut inside before testing Raya with both teams now searching for a winning goal.
Bees sub Tariqe Fosu was next to threaten when he forced Schofield into a near-post parry from 15 yards before Mathias Jensen's deliciously inviting free-kick flashed across the face of the home goal without any of his team-mates applying a finishing touch.
Norgaard's edge-of-the-box half-volley also drifted wide, but the hosts held on against the Football League's leading marksmen to inch eight points clear of the relegation zone despite a run of two wins from 17 matches.
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