Wednesday looked the sharper side for an hour, but it all went wrong for new manager Gary Megson in his second game in charge of the Owls in a disastrous five-minute spell when they conceded goals from Lateef Elford-Alliyu and Ian Goodison and had Giles Coke dismissed.
Coke was shown a straight red card for his crude challenge on John Welsh in the 64th minute, while Enoch Showunmi fired home a third goal for Tranmere in the 81st minute.
Wednesday started the second period brightly, but Gary Madine fired over from the edge of the box and another effort was comfortably held by Tranmere goalkeeper Tony Warner. Then the busy striker skimmed the outside of a post with a header from Coke's corner.
Tranmere went ahead against the run of play on the hour with Elford-Alliyu heading in at the far post from Welsh's right-wing cross and it got worse for Megson's side four minutes later with Coke harshly shown a straight red card.
Tranmere doubled their lead from the subsequent free-kick with Goodison heading in from Cresswell's centre in the 65th minute and they stretched further clear with nine minutes to go with an excellent left-footed finish by Showunmi after being set up by Joss Labadie.