The Robins started the match in third and hoping to leapfrog Sheffield United, whose match at Crewe was postponed, into second.
They went ahead after taking advantage of sloppy play by the Bees in the 32nd minute.
Harlee Dean attempted to bring the ball out of defence but his hesitancy was pounced upon by Gary Roberts who played in Simon Ferry and he in turn passed one player before slotting home.
However, the Bees pulled level with 18 minutes left when Clayton Donaldson outpaced his marker and was hauled down in the box by goalkeeper Wes Foderingham.
Sam Saunders then blasted his spot-kick down the middle of the goal before they turned the game on its head four minutes later, Donaldson turning and shooting home from a tight angle.
Tranmere drop to fifth after a 2-0 defeat at Walsall, who have plans to gatecrash the play-offs.
The Saddlers went ahead five minutes after the break when Danny Holmes upended Febian Brandy and Will Grigg coolly slotted home the resulting penalty.
They doubled their lead out of nowhere, Craig Westcarr allowed to run with the ball before smashing an unstoppable shot into the goal.
Yeovil squandered a two-goal lead to draw 2-2 with Crawley although they went level on points with Tranmere.
The Glovers made the ideal start with a fourth-minute opener, Byron Webster heading Ben Gordon's cross high into the net.
Paddy Madden slid the ball low into the corner to put the Glovers further ahead (18).
Crawley pulled one back with less than a minute of the second half gone as Joe Walsh headed home.
The visitors then levelled when they broke and Matthew Sparrow fired under the goalkeeper.
Just weeks ago Bournemouth topped the table but five successive defeats had seen them drop to seventh.
However, their bid to get back in the play-offs was boosted when Brett Pitman placed a 38th-minute penalty into the bottom right-hand corner at Stevenage for the only goal of the game.
The hosts lost Darius Charles following his second yellow card in injury time.
An injury-time equaliser by Carl Baker saw Coventry claim a 2-2 draw with Colchester.
Both teams are in need of points at different ends of the table but Gavin Massey put Colchester ahead before Michael Smith doubled the lead.
Callum Wilson reduced the deficit before Baker's late strike.
Preston won 1-0 at Notts County thanks to Haydn Hollis' own goal 11 minutes before the break, Shaun Batt scored the only goal as Leyton Orient beat Portsmouth 1-0 while an own goal by Antony Kay saw Shrewsbury claim a 3-2 win at MK Dons.