Harry Cornick came off the bench to score the only goal of the game against Swansea and lift Luton to within three points of the Sky Bet Championship play-off places.
The striker scored his first goal for three months, and eighth of the season, to leave sliding Swansea with just one win in their last seven games.
By contrast, Luton have won four of their last seven.
Swansea had given a debut to goalkeeper Andy Fisher, a £400,000 signing from MK Dons during the transfer window, but failed to give him a reassuring welcome.