There was a high-speed tempo to the start of the match as Arjan De Zeeuw and Ellery Cairo made their first league starts for Coventry.
In-form Dele Adebola gained possession after the ball had got caught under the studs of former Sky Blues defender Louis Carey, and when the ball fall to Cairo, the Dutchman's right-wing cross was fired wide by Adebola.
Leon McKenzie chased down Lee Johnson on the byline near the goal but his shot from an acute angle was blocked and Robins keeper Adriano Basso bravely dived to deny Adebola.
The unbeaten visitors responded by grabbing the lead in the 15th minute. Elliott Ward failed to clear Brian Wilson's right-wing centre and Michael McIndoe turned the defender before firing the ball home from six yards.
Bristol City could have extended their lead when McIndoe swung a free-kick into the box and Stephen Hughes cleared before defender Liam Fontaine could pounce.
Marcus Hall then played a free-kick into the area and De Zeeuw's header was heading towards an empty net until Bradley Orr recovered to hack the ball away.
Bristol City's Wilson cut inside to fire a 20-yard strike straight at the keeper and Hughes did likewise for Coventry but from just inside the area.
The visitors made the game safe by grabbing a second goal in the 74th minute. A corner from McIndoe on the right caused havoc in the box and the under-pressure Dimitrios Konstantopoulos punched the ball into the net.
The Greek keeper then produced a fine one-handed save to deny Robins substitute Scott Murray.
However, fellow substitute Darren Byfield did find the back of the net with a close-range strike in the third minute of stoppage time.