Tranmere produced a fine performance in their home FA Cup third round tie but it wasn't enough as a late goal from Wolves earned them the win.
Rovers showed all the effort and determination of recent weeks and could easily have been ahead by half time. Further chances came in the second half but some fine goalkeeping and errant finishing meant the Premier League side were still in the game and Matt Jarvis' strike proved the difference between the sides.
Les Parry named an unchanged team from the one that faced Carlisle six days earlier, with Zoumana Bakayogo, Paul McLaren and John Welsh all recovering from knocks.
Rovers started the game brightly with Terry Gornell and Craig Curran quick to close down the Wolves defence and their persistence earning Gareth Edds a shooting chance on four minutes, but his effort went straight to Welsh international goalkeeper Wayne Hennessey.
Luke Daniels had to react quickly to punch clear a dangerous Wolves corner on 16 minutes and the visitors had two more corners in quick succession on 25 minutes but both were cleared by Paul McLaren.
A sparkling counter attack on 32 minutes brought the closest either chance had come to a goal. Ian Goodison raced up the left to receive the ball from John Welsh and the pair exchanged passes twice with Goodison superbly side stepping Richard Stearman before Welsh's attempted chip was caught by Hennessey.
The move fired the home fans and players, and within two minutes the Wolves keeper had been forced into fine saves to keep out shots from Edds and Walsh. From the corner that followed Welsh's bottom corner bound effort Ian Thomas-Moore came agonisingly close to netting, but his header was cleared off the line by Kevin Foley.
Rovers were nearly punished for not taking their chances, with Wolves quickly racing up the other end and creating a good chance for Matt Jarvis but his close range shot went wide of the target.
Luke Daniels produced an excellent one handed save to keep out Sylvan Ebanks-Blake's close range header ten minutes into the second half after the visitors started the period at a high tempo.
At the other end McLaren shot high over the bar while Gornell's header at Hennessey was adjudged to have been offside.
As the already cold temperatures continued to drop Tranmere had a golden chance to open the scoring. Gornell challenged Hennessey for the ball which broke loose six yards out and the striker reacted fastest but his shot hit the side netting.
Curran volleyed wide with his left foot from 12 yards as Rovers pressed forward, and the striker did well to force a corner on 74 minutes, with Mancienne heading behind.
At the other end Goodison was getting his head in the way of almost every Wolves cross and the defender raced out of his area to take the ball from Jarvis on 75 minutes.
However, the visitors took the lead two minutes later. A through ball went between Taylor and Goodison and into the path of Jarvis who shot first time into the bottom right corner from 12 yards.
Gornell and Welsh were replaced by Chris Shuker and Michael Ricketts with just under ten minutes remaining, with Shuker winning a corner following a long run on the left wing.
The set piece almost brought the equaliser with the ball falling to Curran at the far post only for Hennessey to block his shot.
Tranmere: Daniels, Logan, Taylor, Goodison, Bakayogo, Edds, McLaren, Welsh (Ricketts 84), Thomas-Moore, Gornell (Shuker 84), Curran. Substitutes not used: Collister, Cresswell, Broomes, Barnett, Fraughan.
Wolves: Hennessey, Stearman, Craddock, Henry, Ebanks-Blake (Elokobi 89), Ward, Jarvis, Iwelumo (Vokes 76), Milijas (Halford 89), Mancienne, Foley. Substitutes not used: Surman, Hahnemann, Jones, Zubar.
Referee: Lee Probert