West Ham spoiled Luton's Kenilworth Road homecoming, securing a 2-1 victory on Friday Night Football.
Premier League football was at the famous old ground for the first time after redevelopment works saw Rob Edwards' side start the season with trips to Brighton and Chelsea, and Luton, with the home fans right behind them, made life uncomfortable for West Ham in the early stages.
However, the Hammers battled to win a foothold in the game and their quality shone through just before the interval as Lucas Paqueta's cross picked out Bowen, who powered a head through Thomas Kaminski at his near post (37)
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Luton produced a spirited display and went close to an equaliser through Elijah Adebayo in the second half, but the Premier League new boys lacked quality in the final third. They were eventually punished when Zouma rose highest to head home James Ward-Prowse's corner (85) as West Ham looked to be comfortably heading to the top of the table.
Mads Andersen's late header (90+2) added some late drama and the hosts thought they might have had a penalty after a late shout for handball against Ward-Prowse, but West Ham survived a nervy finish as Edwards' side's difficult start to the season continued.
Luton stay bottom and continue to search for their first points of the season, while West Ham move to the top of the Premier League as their unbeaten start continued.
How West Ham spoiled the Luton party...
Roared on by a raucous home crowd, Luton came out of the blocks quickly. They pressed high and snapped into tackles with the home fans responding every time Edwards' side won the ball back.
It wasn't a comfortable opening for the visitors as Nayef Aguerd's back pass was nearly intercepted by Adebayo and Alphonse Areola looked uncomfortable spilling Ryan Giles' cross.
Luton had their tails up and Ross Barkley had their first real chance of the game as he created space in the penalty area for a shot, but the midfielder dragged his effort well wide of the target.
West Ham gradually began to get a foothold in the game as the half wore on. Both Bowen and Said Benrahma shot wide, but the pressure began to build on the hosts and the breakthrough came just before the break.
Paqueta's superb cross picked out Bowen at the far post and the winger powered a header through Kaminski to spark the away end into life.
Luton responded well to going behind as Adebayo fired over the bar before Carlton Morris' looped a header over Areola and over the crossbar. Tahith Chong also went close as he failed to bundle the ball home at the far post as the hosts threatened at a corner.
It gave Edwards' side hope after the break, but they just could not repeat their first-half performance at the start of the second. It was West Ham who came out with the momentum, and they were denied a second by VAR with Michail Antonio offside in the build-up to Emerson's strike beating Kaminski.
West Ham were building up a head of steam and the hosts needed Ross Barkley to cut out Ward-Prowse's low cross with Benrahma waiting at the far post.
But with the difference between the sides still just one goal, Luton had hope. Marvelous Nakamba's cross reached Adebayo after uncertainty from Aguerd, but the forward's shot could not beat Areola, while Reece Burke headed well over from a corner as the hosts searched for an equaliser.
West Ham looked to have sealed victory when Zouma emphatically headed home a trademark Ward-Prowse header, but Luton hit back with a header of their own in stoppage time through Andersen to bring the game alive once more.
There was more drama to follow as Ward-Prowse suffered a heart-in-mouth moment as the ball appeared to drop on his elbow as he defended a Luton corner, but after a VAR check the penalty claims were dismissed as West Ham held on for victory.
Edwards: Nothing to fear for Luton
Luton boss Rob Edwards: "I can't keep saying the same things but the goals we conceded were disappointing. We kept pushing to the end but it was a tight game and we could have come away with something.
"We know it's a big task, we know it's difficult but there was nothing in the game tonight. We can brush up, we can learn and we will. We'll get back to basics but that's an improvement in the three games.
"There's nothing to fear. I'm glad we've experienced that at home."
On if his side should have had a late penalty, he added: "I'm hearing a lot of noise about it before we came in. If we are on the wrong end of a decision I will be very disappointed as those are huge for us. But I can't stand here and blame it."
Moyes delighted with start of season
West Ham boss David Moyes: "[It was] good. Good against a tough team who are going to put teams under a lot of pressure. Overall I think we did a brilliant job tonight.
"It's not easy to come here and we were under loads of pressure. Thankfully we stood up to it, got a couple of goals and played pretty well ourselves."
On his side's start to the season: "It's incredibly satisfying. I have got to say I am happy with the results [at the start of the season].
"I think for any team you want to get a good start to the season. It makes things a lot easier and gives players more confidence."
Nev impressed with West Ham's quality
Analysis from Sky Sports' Gary Neville at Kenilworth Road:
"I was really impressed with the spine of West Ham. If you look at Antonio at the top, then Zouma at the back, Alvarez and Ward-Prowse in the middle, Paqueta floats - that's a really strong spine.
"David Moyes was under massive pressure last season. He looks like he's got something he can really build on now, and have a really good season."
On Paqueta's performance, he added: "They've used the Declan Rice money wisely. There are clubs in the past who have had that level of money come in who haven't. What they've done with Paqueta is establish they've got an £80m player, which has put an aura around him.
"That's made them feel so much better about having him. For the time being, they need to just enjoy him, he's so graceful on the ball. I love the way he rolls passes into players on the right side, away from defenders. He really is a good player."
Story of the match...
Player of the match - Kurt Zouma
Analysis from Sky Sports' Jamie Carragher at Kenilworth Road:
"I thought Kurt Zouma was outstanding at both ends of the pitch. His spring, and how high he gets up, he's so dominant, especially defensively because that's his big job.
"I said before the game he's got a huge role to play if West Ham are going to get three points, and him and Nayef Aguerd dealt really well with the long balls. It was a big performance from the captain and got the goal that sealed it."
Analysis: Hatters should take heart from determined display
Sky Sports' Laura Hunter:
"Luton Town's vociferous supporters savoured every moment of their first experience of top-flight football since 1992. They made quite the noise. And while the performance of Rob Edwards' side, certainly at the top end of the pitch, didn't quite match its surroundings for energy and intensity, it did give enough to suggest Luton are going to make life difficult for all that frequent Kenilworth Road this season.
"There is no doubt this campaign is going to be a slog for Luton. They don't have the big money signings or flashy stadium, they haven't spent immense amounts of millions in the transfer window, nor can they afford to - but they do have fighting spirit and tenacity. They aren't here to simply make up the numbers. Luton want to punch above their weight, but will have to deal with the harsh reality of the Premier League sooner rather than later.
"Three games. No points. But no cause for despair. For the majority of the game the Hatters conceded possession and territory, yet still outperformed their guests' expected goals. Edwards has got some tidying up to do in the international break, because life in the big leagues is tough, but don't write Luton off too early. They've got plenty more to give."
Opta stats: Bowen continues scoring run on the road
Jarrod Bowen became the first player to score in each of West Ham's first three away games in a top-flight campaign since Vic Watson in 1930-31. Bowen had scored just three goals in his previous 54 away appearances in the Premier League prior to this season.
This is West Ham's joint-highest points tally after their opening four games of a Premier League season, having also earned 10 points in 1999/00. It is also manager David Moyes' joint-best such start in the competition, also accruing 10 points from four games with Everton in 2006.07.
Luton are only the sixth side to lose each of their first three Premier League games in their first ever season in the competition, after Wimbledon in 1992/93, Swindon Town in 1993/94 (first four), Leicester in 1994/95, West Brom in 2002/03, and Wolves in 2003/04.
What's next?
Luton head to Craven Cottage after the international break to face Fulham on Saturday September 16. Kick-off 3pm.
West Ham return to the London Stadium on the same Saturday where they will host Manchester City at 3pm.