The Sky Blues were in complete control in the first half and the only disappointment for manager Mark Robins was the fact they only had one goal to show for their dominance.
Gary McSheffrey shot wide after a strong run in the fifth minute before full-back Cyrus Christie forced Owain Fon Williams into a smart stop shortly afterwards after cutting in from the right.
The home side took the lead in the 19th minute when Carl Baker floated a corner to the back post which Richard Wood headed straight into the path of a grateful Clarke and he volleyed home from close range.
Clarke should have doubled City's lead nine minutes before the break but he headed straight at Fon Williams from Baker's cross.
Tranmere could only improve in the second half - and they did - but it was still Coventry who were on top and McSheffrey went close on three occasions.
The closest Ronnie Moore's team came to an equaliser was a goalmouth scramble in the 71st minute which began with an Ash Taylor header being saved, but the home side eventually cleared.
Joe Murphy made a fine save in the dying minutes to deny Zoumana Bakayogo.