Ryan Lowe netted a 12th minute opener from the spot with a Conor Thomas own goal just after the break and one from substitute Jake Kirby with City loanee Michael Petrasso pulling back a concolation goal with 12 minutes to play.
Sky Blues boss Steven Pressley rang one enforced change to the side that went down 2-1 to Carlisle United at Sixfields, bringing in Billy Daniels to replace recalled Arsenal loan striker Chuba Akpom.
Despite the revised 4-3-3 system to counter a lack of fit strikers, City appeared full of energy and enthusiasm in the opening stages but it was Tranmere who very nearly took the lead on seven minutes.
Jason Koumas drew a foul on the right from Jordan Clarke and swung in a delivery which picked out Stephen Arthurworrey whose goalbound header was kept out by a superb save from Joe Murphy.
The home side got the opener five minutes later though from the spot when Liam Ridehalgh burst into the City area and went down under a challenge from Billy Daniels.
Rovers top scorer Lowe then stepped up to convert the penalty, sending Murphy the wrong way.
Koumas very nearly added a second in dramatic fashion after 21 minutes when his inswinging corner beat the reach of Joe Murphy only to clip the outside of the far post.
City were denied an equaliser just after the half hour though when Clarke's free kick deflected into the path of Carl Baker whose effort was tipped over the bar by Fon Williams.
The Tranmere 'keeper also did tremendously well to keep the hosts in front from the resulting corner, first to stop a rasping shot from Baker and then, when Fleck picked up the loose ball and squared it across the box, Fon Williams made solid saves to deny Daniels and Franck Moussa from close range while still on the floor.
With City still wondering how they were still behind, Tranmere very nearly managed a smash and grab second with a swfit counter attack from Matthew Kennedy who slipped in Koumas to fire into the side netting from 12 yards.
Rovers did their second in cruel fashion two minutes after the break though. Koumas fired in a waist high free kick delivery from the right which cannoned off Conor Thomas and went into the net past Murphy for an own goal.
Four minutes after the hour mark Tranmere forced their advantage home and added a third courtesy of recently introduced substitute Jake Kirby.
A long ball beat the head of Andy Webster and bounced into the path of Wallace who got to the byline before pulling a ball back for Kirby to leave him with a simple finish three yards out.
A full set of substitutes appeared to inject more energy into the City side though and they were given a glimmer of hope with 12 minutes to go.
Sub Mark Marshall floated a pinpoint ball over the top of the back four for Petrasso to run onto and slot a finish through the legs of Fon Wiliiams.
The goal was as close as the Sky Blues got to closing the gap though despite pressing through the six added minutes as Tranmere saw the game out to ease their relegation worries.
Attendance: 5,279 (912 Sky Blue Army)
Coventry City: Murphy, Chistie (Willis 73), Webster, Seaborne, Clarke, Fleck, Thomas, Petrasso, Moussa, Daniels (Marshall 67), Baker (c) (McGeouch 76)
Subs: Burge (GK), Adams, Barton, Maund
Tranmere Rovers: Fon Williams, Taylor, Wallace (c), Lowe (Kirby 58), Cassidy (Stockton 67), Jennings, Kennedy (Robinson 86), Koumas, Ridehalgh, Pennington, Arthurworrey
Subs: Mooney (GK), Holmes, Goodison, Power