They were in control and looking to give Kevin Bond only his second success in 11 matches as manager when Lee Johnson struck.
The little midfielder had been on the verge of being substituted by his dad, City boss Gary Johnson, when he produced a wonder-pass for Scott Murray to run past Neil Moss in the Bournemouth goal.
Then, with the visitors on the back-foot from a corner, Johnson, from 30 yards, fired a low shot through a host of players to score his first goal for City.
Bournemouth, with Darren Anderton suspended, and several players injured, had taken the lead from a first-half free-kick.
Marcus Browning added to it early after the break when Adriano Basso completely missed his attempt to fist away a right-wing cross from Shaun Cooper.
Before City's unexpected fight-back sub Sam Vokes missed a wonderful chance to make it a three-goal lead.
Early on Bournemouth had looked for a penalty when James Hayter was tipped over just inside the area but referee Jamil Singh was completely unsympathetic.
Two minutes later, though, he gave Hayter a free-kick a couple of yards outside the area. Hit hard into the wall by Simon Gillett, it bounced off to the unmarked Brett Pitman, and the Channel Islander hit it across the keeper and in behind the far post for his third goal this season.
There could have been another for Bournemouth when Johnson lost the ball in midfield but Cooper was a yard off-target with his shot.
City came back strongly but their game lacked width and until Lee Johnson produced his moments of magic the game looked beyond them.
Starting only his second game in three months striker Steve Brooker was at the heart of just about everything City did.
He lobbed one volley wide and then saw a header desperately turned over the bar by Moss for a corner.
But Brooker, who ran himself virtually to a standstill, found little support until Jennison Myrie-Williams was sent-on to bring to verve and pace down the left flank.