The hosts had come close to opening the scoring, but defender Ben Cabango was denied when his header struck the post.

The win lifts Luton up to ninth, while Swansea slip to 19th, albeit with a 12-point cushion above the drop zone.

Swansea boss Russell Martin reacted decisively to his side's 2-0 defeat at Hull, making five changes to his starting line-up, including giving a debut to goalkeeper Andy Fisher and resting top scorer Joel Piroe.

Welshman Nathan Jones made two changes to the side that held Blackburn Rovers, with Danny Hylton recalled, while new signing Jed Steer was on the bench.

Luton started brightly with Hylton just failing to connect with James Bree's threatening free-kick, but it was Swansea who should have opened the scoring as goalkeeper James Shea did brilliantly to deny Michael Obafemi with his feet after Matt Grimes' defence-splitting pass.

The half then began to meander other than a blocked effort from Olivier Ntcham, before Luton missed three good chances to take the lead just before the break.

The Hatters were a real threat from set-plays and Hylton was close to an opening goal as he headed just over from another Bree free-kick.

Reece Burke also came close before the interval with a dipping shot from outside the area that was just over, before Allan Campbell headed over, unmarked, with the final action of the half.

Swansea - who lost defender Kyle Naughton to a groin injury - increased their tempo after the break and came close to scoring on 55 minutes when Cabango's header hit the post, with defender Ryan Bennett only able to turn the rebound wide after Hannes Wolf's cross.

Wolf also came close with a shot across goal on 70 minutes, but Swansea were behind moments later.

Substitute Cornick was the man to break the deadlock on 72 minutes and he did so with a fine first-time finish after Cameron Jerome's neat pass inside.

Swansea tried to respond and substitute Joel Piroe headed straight at Shea from Ryan Manning's cross, but the Welsh club are not in good form, having collected just five points in the Championship since 27 November, and were booed off by their supporters at full time.

Swansea City head coach Russell Martin said:

"I think we were the better team. We had three huge chances and don't score. They don't cause us much harm. They're really good at what they do, you can see why they're doing so well in the league.

"But we have to score when we're on top... so I'm really disappointed.

"I didn't see many problems with the performance in general. I thought we were dominant. When we beat the press we looked really dangerous. The lads are giving us everything they've got.

"We concede such a poor goal. It's so disappointing. You can't concede a goal like that."

Luton Town boss Nathan Jones said:

"It's a massive win, Swansea are such a tough side to play against, so hard to get the ball back against.

"The tactical awareness was wonderful. We were strong, aggressive, disciplined and clinical.

"Game-changers came on and won us the game, so it was a complete away performance.

"To come here and win 1-0 is a wonderful. I loved our performance tonight."