Carlos Vinicius scored after coming off the bench to give Fulham a 1-0 victory and inflict a fourth consecutive Premier League defeat on Luton.
Marco Silva earned a 50th win on his 100th game in charge of Fulham as they chalked up their first home three points of the season.
The hosts were frustrated for large periods at Craven Cottage by Luton, who came closest to scoring in the first half when Jacob Brown headed against a post.
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But Fulham stayed patient as they dominated possession in the second half, eventually seeing Vinicius break the deadlock with a simple tap-in in the 65th minute, just three minutes after coming on.
The result means Luton are still seeking their first Premier League points following promotion from the Championship.
How Fulham beat Luton
Fulham dominated possession throughout the first half yet could not create any clear-cut opportunities from open play. They only went close with Kenny Tete's glancing header at the near post from Andreas Pereira's corner.
Luton soaked up the pressure and then created their best chances within two minutes of each other. First, Carlton Morris volleyed wide when the ball dropped to him in the box and then Brown headed against the right-hand post from Issa Kabore's cross.
On the stroke of half-time, Morris went down off the ball in the area at a free-kick after grappling with Harrison Reed, but nothing was awarded.
The visitors sparked Fulham into life at the start of the second half once Bernd Leno had saved Amari'i Bell's volley.
Joao Palhinha saw his header drop on the roof of the net before Vinicius stabbed home from close range after Thomas Kaminski parried Willian's cross into the path of the striker.
Willian then saw an effort of his own deflect behind before Vinicius was denied late on with Luton unable to find an equaliser as Tom Lockyer glanced a late chance wide.
Silva: Luton showed respect with approach
Fulham manager Marco Silva: "It was a tricky, difficult one and we expected that. We expected 5-3-2 always behind the ball and they did it differently with 5-4-1. Nine players always around the box, really deep.
"It's not something we face every week at this level, probably three years ago you faced it. This season, last season it is the first time but we have to get used to that. It showed the respect they had.
"In the first half, we lacked some dynamic to create chances when you have the ball a long time. Second half, some improvements. The two changes made an impact in the game.
"Overall we were the best team on the pitch and deserved the three points."
Edwards: Is there a different rule for Luton?
Luton manager Rob Edwards: "I'm very proud of the lads, we missed three golden opportunities today. Brownie's header hitting the woodwork, Amari'i's (Bell) one and Tom Lockyer's one right at the end. Three big chances.
"We should have had a penalty as well. It was a foul on Carlton Morris from the wide free-kick, (Harrison) Reed is not looking at him. Anywhere else on the pitch, it's a foul.
"Bell had one given one against him not long before. Inside the box or outside the box, is there a different rule? Maybe it's just one for Luton?
"We could be talking about a very different result."
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How the match played out
Opta Stats - Palhinha the duel master
- Fulham had 77.8 per cent possession against Luton Town, the most amount of possession they have had in a Premier League game since records began (2003/04).
- Luton Town have now lost their first four matches of a league season for the first time since 2002-03, when they lost their opening four in the third tier.
- Fulham's Joao Palhinha won 11 duels today, the most of any player. Since making his Premier League debut in August 2022, he has won 308 duels, more than any other player in this time.
- Only Wolves (10) have conceded more goals in the second half of Premier League matches this season than Luton Town (7), with the Hatters conceding after half-time in all four of their matches.
What's next?
Fulham's next game is a trip to Crystal Palace on Saturday - kick-off 3pm. Marco Silva's side then host Norwich in the Carabao Cup on September 27 - kick-off 7.45pm.
Luton's next outing is at home to Wolves on Saturday - kick-off 3pm. The Hatters then travel to Exeter in the Carabao Cup on September 26 - kick-off 7.45pm.