When full-back Jamie McAlister drove a 25-yard shot from a corner into the roof of the net it was only his second goal for the Robins in 114 starts.
With their resistance stunted Coventry then fell to a break-out from a free-kick, Lee Johnson tapping in the killer goal after a long run into the box by Gavin Williams.
An open game was noteworthy for tackles on the flying side of enthusiasm, but brought no cautions until late on, although referee Phil Crossley had a long lecture for McAllister and Coventry's Michael Doyle after one touchline clash.
It was one he was to repeat in the second half after the flare-up between Leon Best and one-time Coventry defender Louis Carey.
Playing with three centre-backs Bristol found plenty of opportunity to press forward from the midfield. But too many of their shots were long-range, although Michael McIndoe found plenty of power behind two of his efforts.
When Coventry managed to get their attack going a promising three-man move involving Best, Freddie Eastwood and Marcus Hall founded on the firm head of central defender Jamie McCombe near the penalty spot.
McCombe was also close to scoring when he went up for Bristol's third corner, Keiren Westwood bringing off a fine double save.
Coventry were disappointed when a header from Best crossed the line only to be ruled out by an infringement from James McPake.
But the closest miss of all saw Stern John's header against his old club kicked off the line by Hall.
Coventry were giving everything to the game and were out of luck when Eastwood pulled a shot wide of the far post.
It was their final effort as the fast-moving affair went Bristol's way.