Burnley manager Vincent Kompany said it "felt great" and was "very proud" of his side after they gained a dramatic win at Luton Town for their first Premier League victory of the season.
Jacob Bruun Larsen cut in from the right and unleashed a stunning shot into the far top corner in the 85th minute for what proved to be the winner.
That came only 65 seconds after Luton had equalised, substitute Elijah Adebayo finishing after Reece Burke had headed on Tahith Chong's cross.
Burnley had only gained one point from a tough opening six games of the season and went ahead at Kenilworth Road when Lyle Foster produced a composed finish after fine work from Sander Berge in first-half stoppage time.
"We had to battle for it and I am proud of the team for what they showed," said Kompany following his first Premier League match victory as a manager after helping Manchester City win the title four times as a player.
"It feels great, three points in the Premier League. This is a team that enjoys this type of work. We loved everything about it," he said.
"It is a game that deserved its place in the Premier League, with two teams who showed they will give everything this season.
"It's nice to win as a manager I've had the experience of winning [as a player] so I'm alright."
Burnley's win means Bournemouth and Sheffield United are the only sides yet to win in the top flight in 2023-24.
Kompany's team won the Championship last season, before Luton also earned promotion from the second tier by beating Coventry City on penalties in the play-off final.
Luton Town v Burnley as it happened, plus reaction and analysisLuton fans, have your say on the gameBurnley fans, share your thoughtsBurnley up and running, but Luton left deflated
Luton came into this match after winning 2-1 at Everton on Saturday, but could not build on that victory as Burnley fought back from the disappointment of conceding a late equaliser to almost immediately score the decisive goal.
This match had originally been scheduled to take place in August but it had to be postponed as redevelopment work on Luton's Kenilworth Road stadium had not been completed.
The home fans nearly got to celebrate a bizarre goal in the opening 60 seconds when Burnley goalkeeper James Trafford saw his clearance charged down by Carlton Morris, only for the ball to go just wide.
The Clarets then had the better of the first half.
Foster rushed a shot when in a good position, Josh Cullen fired over from 15 yards and Zeki Amdouni had a header pushed over the crossbar by Thomas Kaminski.
Amdouni then shot over with only Kaminski to beat, before the visitors took a deserved lead in the second minute of injury time with Foster converting for his third goal of the season from Berge's through ball.
But Luton, a constant threat at set pieces, were much better after the restart as they piled on the pressure looking to earn only their second home point of the season.
The Hatters had an effort cleared off the line when Pelly Ruddock Mpanzu's cross was met by Jacob Brown's header but Cullen was well placed to superbly deny the hosts a goal.
Luton wanted a penalty after Morris went to ground, but, following a lengthy video assistant referee check, it was judged that Jordan Beyer had got a touch to the ball.
Rob Edwards' side did make the breakthrough with six minutes left, only for their hopes to be dashed soon afterwards as Burnley then held on to join Luton on four points after seven matches.
"I am really proud of the players and the performance, I thought they gave everything," said Edwards.
"They shaded the first half, but in the second we completely dominated them, threw everything at them. We had 15 shots inside the box and scored once so that is an area we know we can improve in.
"If the performance is right you give yourself a chance of getting points on the board. If we don't perform we have no chance this year.
"We performed well and lost which shows the task we have.
"We will have disappointments this season and we need to be able to stick our chests out, believe in what we are doing. We are all pulling in the same, right direction.
"The fans will stick with us when they see us putting that effort in. They are proud of these players."
Player of the match
Bruun LarsenJacob Bruun Larsen
with an average of 8.50
Luton Town
Squad number7Player nameOgbene
Squad number24Player nameKaminski
Squad number9Player nameMorris
Squad number11Player nameAdebayo
Squad number13Player nameNakamba
Squad number19Player nameBrown
Squad number45Player nameDoughty
Squad number4Player nameLockyer
Squad number15Player nameMengi
Squad number14Player nameChong
Squad number29Player nameBell
Squad number12Player nameKaboré
Squad number16Player nameBurke
Squad number17Player nameMpanzu
Burnley
Squad number34Player nameBruun Larsen
Squad number17Player nameFoster
Squad number8Player nameBrownhill
Squad number24Player nameCullen
Squad number16Player nameBerge
Squad number5Player nameBeyer
Squad number3Player nameTaylor
Squad number25Player nameAmdouni
Squad number30Player nameKoleosho
Squad number28Player nameAl Dakhil
Squad number14Player nameRoberts
Squad number9Player nameRodríguez
Squad number21Player nameA Ramsey
Squad number44Player nameDelcroix
Squad number1Player nameTrafford
Line-ups
Luton
Formation 3-4-2-1
24Kaminski15Mengi4Lockyer29BellSubstituted forBurkeat 21'minutesBooked at 59mins12KaboréSubstituted forAdebayoat 62'minutes17Mpanzu13NakambaBooked at 90mins45Doughty19BrownBooked at 36minsSubstituted forChongat 69'minutesBooked at 90mins7Ogbene9MorrisSubstitutes
5Andersen8Berry10Woodrow11Adebayo14Chong16Burke23Krul26Giles38JohnsonBurnley
Formation 4-3-3
1Trafford14RobertsBooked at 66mins28Al Dakhil5Beyer3TaylorBooked at 90mins16Berge24Cullen8Brownhill30KoleoshoSubstituted forBruun Larsenat 75'minutes17FosterSubstituted forRodríguezat 80'minutes25AmdouniSubstituted forA Ramseyat 74'minutesSubstituted forDelcroixat 90+4'minutesSubstitutes
4Cork9Rodríguez21A Ramsey22da Silva31Trésor34Bruun Larsen44Delcroix47Odobert49MuricReferee:Peter Bankes
Attendance:10,918
Live Text
Match ends, Luton Town 1, Burnley 2.
Second Half ends, Luton Town 1, Burnley 2.
Attempt missed. Tom Lockyer (Luton Town) header from the centre of the box misses to the right. Assisted by Alfie Doughty with a cross following a corner.
Corner, Luton Town. Conceded by Ameen Al Dakhil.
Charlie Taylor (Burnley) is shown the yellow card.
Foul by Josh Brownhill (Burnley).
Marvelous Nakamba (Luton Town) wins a free kick in the defensive half.
Substitution, Burnley. Hannes Delcroix replaces Aaron Ramsey.
Marvelous Nakamba (Luton Town) is shown the yellow card.
Tahith Chong (Luton Town) is shown the yellow card.
Josh Cullen (Burnley) wins a free kick in the defensive half.
Foul by Carlton Morris (Luton Town).
Attempt missed. Jay Rodríguez (Burnley) right footed shot from outside the box misses to the left.
Attempt missed. Carlton Morris (Luton Town) header from the centre of the box misses to the right. Assisted by Alfie Doughty with a cross following a corner.
Corner, Luton Town. Conceded by Sander Berge.
Offside, Luton Town. Carlton Morris tries a through ball, but Elijah Adebayo is caught offside.
Goal! Luton Town 1, Burnley 2. Jacob Bruun Larsen (Burnley) left footed shot from outside the box to the top left corner. Assisted by Connor Roberts.
Goal! Luton Town 1, Burnley 1. Elijah Adebayo (Luton Town) right footed shot from the centre of the box to the bottom left corner. Assisted by Reece Burke with a headed pass.
Attempt blocked. Jay Rodríguez (Burnley) right footed shot from the left side of the box is blocked.
Substitution, Burnley. Jay Rodríguez replaces Lyle Foster because of an injury.
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