Chris Burke's double secured all three points at Ashton Gate as Blues moved up to 14th in the table, four points off the play-offs with at least two games in hand on those around them.
They travelled to Club Brugge in the Europa League on Thursday but their European campaign is showing no sign of taking a toll on their Championship form.
The Blues boss said: "Bristol were right up for the game with a new manager and we had to show a different side to us than was on show in Belgium on Thursday.
"They got in a lot of crosses and we had to defend really solidly.
"Now there is a hard week ahead with games against Leeds and Brighton.
"Some of our fans probably came straight to Bristol from Belgium. I'm delighted that we were able to score the final goals in both games at their end because they are hugely important to us.
"We are on a roll at the moment and who knows how long it will continue."