Paul Ince's superb goal two minutes from time gave Wolves the win to propel them into the play-off places.
Mark Davies' instinctive finish had put Wolves ahead just before the hour, but Steve Howard's bravely headed equaliser seemed to have given Luton a point.
But Ince, lurking on the edge of the box, crashed a wonderful half-volley past Luton goalkeeper Marlon Beresford.
Davies' strike, a precise close-range volley, was the 17-year-old midfielder's first goal for Wolves.
Wolves manager Glenn Hoddle:
"It's the first time we've won when we haven't played well and that's a good sign.
"If we go on a run - and we're capable of doing that - then we can consolidate this play-off position.
"We had to make sure we won even if it was a bit 'ugly' and I'm delighted."
Luton manager Mike Newell:
"It's been the story of our season away from home.
"It's getting a little bit frustrating because I'm having to say the same things week in, week out.
"They've scored against the run of play - unless I'm watching a different game we were the better side."
Wolverhampton: Postma, Ross, Edwards, Craddock, Lescott, Kennedy, Davies, Huddlestone, Ince, Cort, Clarke (Ganea 78).
Subs Not Used: Oakes, Anderton, Seol, Ricketts.
Goals: Davies 57, Ince 88.
Luton: Beresford, Edwards, Coyne, Heikkinen, Underwood, Brkovic, Nicholls, Foley, Showunmi, Howard, Vine (Feeney 64).
Subs Not Used: Brill, Barnett, Morgan, Bell.
Goals: Howard 80.
Ref: M Dean (Wirral).