Tranmere pulled a goal back in the 20th minute and laid siege to the Wolves goal for long periods after that but could not find an equaliser.
The visitors were ahead after only 44 seconds, thanks to an awful goalkick from the Tranmere goalkeeper, Danny Coyne. He scuffed the ball straight to the feet of Robbie Keane, who ran in and curled a right-foot shot wide of Coyne.
It was embarrassing for Coyne and he was again unlucky in the 12th minute when apparently unsighted as Fernando Gomez scored Wolves' second goal. Tranmere's captain, Kenny Irons, was at fault this time. He was under no pressure to clear a cross by Mark Atkins but headed straight to Gomez, whose volley went beyond Coyne's despairing dive.
Far from being dispirited, Tranmere produced some superb play, inspired by their midfield dynamo, Alan Mahon, and Santos, who put them back in the match with a glancing header from Mahon's corner.
It was nearly all Tranmere after this but Wolves held on defiantly with fine work in central defence by Neil Emblen and Keith Curle.
Tranmere Rovers: Coyne, Allen, Thompson, McGreal; Challinor, Irons, Mahon, Santos, Parkinson (Jones, 87), Taylor (Morrissey, 75), O'Brien (Koumas, 57).
Wolverhampton Wanderers: Stowell, Atkins, Muscat, Gomez (Richards, 78), Emblen, Curle, Niestroj (Connolly, 53), Robinson, Corica (Sedgley, 40), Keane, Gilkes.
Referee: K Lynch (Knaresborough).