Paddy Madden notched his eighth goal in his last five appearances in the final minute of the first half to cap a swift counter-attack and take the points.
Moments before Leon Clarke wasted the hosts' best chance when he failed to make a solid enough contact after beating goalkeeper Marek Stech to a through ball.
The visitors proceeded to break and Madden applied a cool low finish when one-on-one with the goalkeeper.
The Sky Blues dominated the second half in search of an equaliser. Striker Stephen Elliott came off the bench and hit the crossbar with his first meaningful involvement, after a neat one-two with Franck Moussa.
Elliott went close again in the 80th minute, but his low shot from the right-hand side of the box slid across the goalmouth and narrowly wide.
Coventry captain Carl Baker, who had a goal ruled out in the 10th minute for offside, also had two opportunities to level, but smashed the ball over with his first shot before stinging the palms of Stech.