James Collins scored his 12th of the season to claim a deserved and vital three survival points at promotion-chasing Swansea.
The towering 73rd minute header lifted them off the foot of the Championship table, cut the gap to safety to two points and proved the icing on the cake of a consummate away performance from the Hatters.
They had the better of the contest bar the first 15 minutes of the second half at an empty Liberty Stadium, without threatening too much. But they were solid and comfortable at the back thanks to a classy Cameron Carter-Vickers display, while Glen Rea in front of the central defender made his 150th appearance for the club.
Forward Harry Cornick, who saw plenty of the ball, should have edged them in front after he did all the hard work to jink into space but lifted his angled drive high over the bar.
Swansea were much improved after the break, penning Town in their own half but they only fashioned the one clear opening, which saw goalkeeper Simon Sluga pull off a reflexive one-handed save to keep out Ben Cabango’s close range header, with Liverpool loanee Rhian Brewster heading over the rebound.
Before that, Town were unlucky to be incorrectly on the wrong end of a linesman’s flag as Cornick was played in, but his side sparked back into life from the hour mark as the substitutes played a part.
First James Bree saw a shot on the turn blocked and then Izzy Brown – one of three players demoted to the bench – whipped in a teasing cross that Collins attacked.
The striker was hungrier than both Connor Roberts and Cabango, getting in between the defenders to deliver a powerful header that proved too hot to handle for goalie Freddie Woodman.
The Jacks let their tempers get the better of them and Jordan Garrick boosted Town when he was shown a red card in the 83rd minute. A melee broke out following a series of rash challenges in one hot-headed passage of play from the hosts and the home substitute was seen to throw a punch at Collins.
But, despite a monster nine minutes of time added on, Luton saw out the contest to claim their fourth away win of the campaign to remain unbeaten since their return from football’s three-month Coronavirus shutdown