The visitors took a two-goal advantage into the half-time interval courtesy of strikes from Franck Moussa and William Edjenguele.
Tom Eastman reduced the deficit for the hosts but David McGoldrick sealed the points for the Sky Blues.
Moussa stabbed home from Gary McSheffrey's low cross after 34 minutes before Coventry doubled their lead in controversial circumstances.
When Carl Baker's cross was headed in by Edjenguele at the far post, the assistant referee's flag was up quickly, with McSheffrey adjudged to have been in an offside position. But after consulting his assistant, referee Trevor Kettle allowed the goal to stand.
Eastman headed in Anthony Wordsworth's free-kick with 19 minutes to go to give the U's hope but McGoldrick secured the win with a tidy close-range finish.