Matt Jarvis was the star of the show for shot-shy Wolves, scoring the only goal of the game on 77 minutes to make up for a terrible first-half miss.
The supposed gulf in class, Premier League Wolves sit 51 places above League One strugglers Tranmere in the football pyramid, was not evident in a dire opening 25 minutes.
Freezing temperatures and an ever-worsening playing surface meant the likes of Wolves hitman Sylvan Ebanks-Blake appeared more interested in keeping his footing than terrorizing the Rovers backline.
But it was Tranmere who finally came to life on the half hour and put their Premiership opponents under pressure - with Wolves goalkeeper Wayne Hennessey saving from Zoumana Bakayogo and Gareth Edds in the space of 60 seconds.
The first clear cut opportunity of the game fell to Tranmere top-scorer Ian Thomas-Moore on 34 minutes, but he was left frustrated as his near post header was cleared off the line by Wolves defender Kevin Foley with Hennessey beaten.
Foley's clearance seemed to stun Mick McCarthy's men into life and Wolves should have taken a first-half lead just two minutes later, but Jarvis produced a contender for miss of the season - somehow firing wide after latching on to Chris Iwelumo's flick-on with just goalkeeper Luke Daniels to beat.
Tranmere goalkeeper Daniels produced a world-class save on 54 minutes to keep his League One side in the tie.
Wolves striker Ebanks-Blake thought his close range header was goalbound, but somehow Daniels got a hand to his header to divert it behind.
Tranmere's Terry Gornell was holding his head in his hands on 65 minutes as he somehow sidefooted wide of an open goal after winning a foot-race to dispossess goalkeeper Hennessey.
Jarvis eventually scored the all-important winner on 77 minutes to send Wolves into round four - slamming the ball home after an impressive through ball from Nenad Milijas.
And it could have been even better for Wolves late on as Sam Vokes went close with a header, while Tranmere's Craig Curran should have done better when he fired straight at Hennessey in the dying minutes.