Zoumana Bakayogo was also kept busy in the opening 45 minutes of the match, making a number of crucial blocks for Tranmere as Coventry pushed for an opening goal.
The home side's efforts were rewarded in the 20th minute, when Leon Clarke fired the ball in from close range to give his side the lead.
Clarke had a chance for a brace in the first half, but Fon Williams was able to keep him out the second time.
Coventry continued to have the better of the chances after the break, while David Amoo looked the most likely to find an equaliser for Tranmere.
Tranmere remain top of the League One table despite the loss, while Coventry climb to 10th.