The home side were on top for most of the game but let their guard down for ten minutes after City striker Danny Haynes had seen red early in the second half.
Haynes can have little argument with the decision - his first yellow for needlessly blasting the ball into the home fans late on in the first half and the second for a late challenge on Bees defender Ryan Dickson.
But the sending off seemed to invigorate the Robins and seven minutes later Liam Fontaine volleyed the ball into a crowded area where Maynard was on hand to head home.
The Bees had enjoyed much the better of the first half and should have gone ahead in the 11th minute when debutant Steve Kabba fluffed a glorious chance while clean through on goal.
Having turned and outpaced his marker he knocked the ball past the onrushing Robins keeper Dean Gerken.
But with the open goal gaping in front of him the 28-year old couldn't keep his balance and sprayed his left-footed finish high over the bar.
Maynard made him pay when he nodded in on 56 minutes.
The Bees took over again after going behind and might have equalised in the 70th minute when midfielder Sam Saunders, a summer acquisition from Dagenham and Redbridge, had a curling free kick parried just round the post by Bristol keeper Dean Gerken.
Moments later the Robins shot-stopper was called into action again, pulling off a one-handed save from another Saunders effort who had been a thorn in the Bristol defence's side all game.
The lively midfielder had one last chance with nine minutes to go but his flicked header from Sam Wood's looped cross bounced agonisingly off the top of the bar.