It might have been different if Wrexham had taken an early chance when Carlos Edwards beat Jason McAteer and crossed into the box, but Chris Armstrong miscued his shot to Chris Llewellyn who fired too high over the crossbar.
Wrexham were down to ten men for a few minutes while Andy Holt was off being treated for a cut lip when a bad mistake by Shaun Pejic let Rovers in and turned the game.
He thought a long ball was running out but Iain Hume chased, kept it in and squared for Chris Dagnall to beat new goalkeeper Xavi Valero from close range.
Tranmere stepped up a gear and Steve Roberts had to clear another shot from Dagnall before Mark Rankine put Hume through to hit inches wide.
Dagnall switched to provider for the second gaol, turning a perfect pass across the area for Hume to clip home.
Wrexham born Gareth Roberts added the third goal early in the second half collecting a headed clearance from Dennis Lawrence and smashing a dipping volley past Valero from 20 yards.
Armstrong raised hopes for the battered Dragons, jabbing the ball over the line in a goalmouth scramble following a corner to reduce the lead, and Carlos Edwards, back form a long injury lay-off, hit over from long range.
It eased the pressure slightly but there was no stopping Tranmere as they went on to add two goals in a minute, Theodore Whitmore hitting home a Hume pass and then turning provider for substitute Paul Hall to finish.