Wolves gratefully accepted a gift from Luton keeper Marlon Beresford to move into the Championship play-off places.
Beresford allowed Karl Henry's speculative shot to slip through his grasp for the softest of winners.
Wolves led through a header from Gary Breen who then deflected Lewis Emanuel's shot past Matt Murray.
Leon Barnett headed Luton in front, but Wolves levelled when Andy Keogh reacted first when Beresford could only parry Michael Kightly's shot.
Luton boss Mike Newell:
"How disappointing can you get? I believe we have lost more leads than any other team in the league.
"We have only ourselves to blame. We have shown we can score goals, but we should not have to score four to win.
"Our fate is in our own hands."
Wolves manager Mick McCarthy:
"I was not happy with the tosh we produced for the 20 minutes before half-time.
"We had good fortune for the winner, thanks to their keeper's mistake. We also had to play the conditions because of the difficult pitch.
"Have we found momentum at the right time? It would appear so."
Luton: Beresford, Foley, Barnett, Heikkinen, Emanuel, Bell, Robinson, Spring (Carlisle 71), Keane, Talbot (Feeney 71), Runstrom.
Subs Not Used: Brill, Davis, Boyd.
Booked: Spring, Robinson, Emanuel, Feeney.
Goals: Emanuel 22, Barnett 45.
Wolverhampton: Murray, Edwards, Breen, Neill Collins, McNamara, Kightly, Henry, Olofinjana, McIndoe, Ward (Bothroyd 76), Keogh.
Subs Not Used: Budtz, Craddock, Clapham, Gleeson.
Goals: Breen 10, Keogh 53, Henry 66.
Ref: P Taylor (Hertfordshire).