Alex Lawless was the match-winner for Luton with a well-taken volley within seconds of the restart after half-time, ensuring the non-league side will be in the hat for Sunday’s fourth-round draw.
It was a deserved victory for the Hatters in front of a sell-out Kenilworth Road crowd, with 59 places separating the two sides in the football ladder.
Both sides enjoyed clear openings inside the first six minutes, JJ O’Donnell firing over from the edge of the penalty area before Kevin Doyle got in behind but could only send his effort just wide.
Bakary Sako flicked an effort off target for Wanderers before Luton were handed a golden opportunity in the 22nd minute.
Wolverhampton-born Andre Gray, released by the Black Country club as a teenager, found himself clean through but, bearing down on Carl Ikeme, saw his effort well saved by the Wolves goalkeeper.
Jon Shaw flashed a good chance across goal and out for a throw-in at the start of the second half, but it was from that throw which Luton notched what turned out to be the winner.
Wolves made a mess of it and a cross was duly sent into the box, Shaw went up for header and the ball fell to Lawless who volleyed into the bottom corner from the edge of the area.
The hosts were firmly on top, O’Donnell drilling over, but Wolves rode the storm and Christophe Berra nodded against the top of the bar at the other end.
Doyle headed straight at Tyler in the 63rd minute but Wolves, devoid of confidence and ideas, were failing to do enough.
O’Donnell was stretchered off after receiving lengthy treatment following an accidental kick to the head by substitute Slawomir Peszko.
And despite nine minutes of injury time, during which Tyler tipped over from Jamie O’Hara, the Hatters ran out winners.