Gavin Massey scored the only goal of the game in the 18th minute, side-footing in from Elliot Lee's fine pass.
Visiting keeper Elliot Parish saved on-loan Norwich player Jacob Murphy's penalty shortly before the interval.
A second Easter win for 23rd-placed Colchester moves them within seven points of safety, while Coventry are eight points adrift of the play-offs.
The Sky Blues have now lost nine of their last 13 matches, to plummet from fourth to 10th.
League One strugglers Colchester United further dented Coventry City's play-off hopes with victory at the Ricoh Arena.