Coventry keeper Kieren Westwood was the star of the show until Jamie McAllister broke the deadlock in the 66th minute with a well-worked goal, only his second in 114 starts.
Lee Johnson's 80th-minute tap-in from a Gavin Williams cross sealed the points.
The result kept the Robins very much in the promotion shake-up, but virtually ended Coventry's slim chance of reaching the play-offs.
Johnson said: "It's one of our most important wins of the season. We really needed that result after the disappointment of two narrow away defeats.
"It was a great strike by Jamie when we needed it most. Coach Keith Millen came up with the set-piece idea in training, and that's why I was first to congratulate him when the goal was scored.
"We can now look forward to a fantastic game against Cardiff here at Ashton Gate on Sunday. There is sure to be a cracking atmosphere, and both teams will be up for it.
"It was a relief when we scored tonight after missing several chances at Derby on Saturday. The way their keeper was playing, I thought it might be another of those games."
Coventry boss Chris Coleman added: "We're going to need a lot of things to go for us to get into the play-off picture now.
"I think the performance was a bit of a hangover from our FA Cup run. It was a good time for Bristol to play us after all the effort and emotion that went into the Chelsea match.
"I thought we started okay, but I was always worried we might run out of steam. The big disappointment was the goals we conceded.
"The first was from a set-piece, and the second stemmed directly from our own set-piece, which was just as bad.
"I think the players gave everything, but it's difficult enough to come here at the best of times, let alone on the back of a huge cup tie."
Westwood kept Coventry in the game with fine first-half saves from Williams, Stern John and Jamie McCombe, while Marcus Hall also denied John with a goal-line clearance.
Leon Best had the ball in the net for Coventry on 43 minutes, but the effort was ruled out for pushing by a team-mate.
Coleman said: "We can't think why the goal wasn't given, and I also felt we had a good claim for a penalty for a push on Best."
Clinton Morrison shot narrowly wide for Coventry early in the second half, but the longer the game went on, the more Bristol looked the likely winners.