City had taken a 1-0 lead through Nicky Maynard but a dubious handball decision against Louis Carey resulted in Adam Johnson levelling for the visitors from the penalty spot.
Johson Delighted With Response
However, Maynard scored his second goal of the game in stoppage time to earn City a 2-1 success againstone of the Championship promotion favourites.
"If we hadn't won I would have said a lot about the penalty" City boss Johnsn said after Saturdays match at Ashton Gate.
"The ball hit Louis on the arm and to be a penalty he had to strike the ball.
"The ball hit Louis on the arm and to be a penalty he had to strike the ball.
"It has been a difficult week but today the lads showed they have the fighting spirit to make a success of the season.
"After our defeat in the Carling Cup to Carlisle the players held their own meeting to put things right."