In a battle between two promoted clubs, Burnley took the lead just before half-time through Lyle Foster, who returned from a three-match ban to score his third goal of the season.
And although the hosts got an 84th-minute equaliser through substitute Elijah Adebayo, Danish winger Bruun Larsen produced an immediate response with a 20-yard curler that takes Burnley level with Luton on four points.
How the match unfolded
While chances were initially hard to come by, Luton lost defender Amari’i Bell to injury in the 21st minute and immediately conceded the first attempt on target as Zeki Amdouni’s near-post header from a corner was tipped over by Thomas Kaminski.
Two passes through the middle of the pitch dissected Luton’s midfield and defence, with Sander Berge receiving the ball in the centre circle, driving forward and playing in Foster, who ran in behind Tom Lockyer and slotted clinically past Kaminski.
Luton were the better team in the second half and created a series of good chances from high balls into the box.
Luton looked set to go three matches unbeaten, and possibly go on to win the match. But instead Burnley hit back in the 85th minute as Bruun Larsen, a summer signing who had come off the bench only 10 minutes earlier, cut inside from the right flank and curled a stunning shot into the top-left corner for his first Premier League goal.