A much-changed Gunners team barely needed to break a sweat to take a two-goal lead into the break, as Martin Odegaard broke the Luton resistance before Daiki Hashioka turned into his own net.
Mikel Arteta's men were on the ropes at a few points during an underwhelming second period, but the visitors' previous penchant for finding the net eluded them as their 18-game goalscoring run in the top flight came to an end.
For just the second time in the 2023-24 Premier League season, Bukayo Saka was nowhere to be seen for Arsenal after his enforced substitution against Manchester City, allowing Reiss Nelson to make his first top-flight start of the campaign.
Thomas Partey, Emile Smith Rowe, Leandro Trossard and Oleksandr Zinchenko were also reinstated to the Gunners' XI as Arteta shuffled his pack, but even a rotated side immediately penned a defence-heavy Luton back.
Rob Edwards fielded every man behind the ball while Arsenal got into their passing flow, initially to good effect, as the hosts failed to find gaps in between the packed Luton defence.
That all changed in the 24th minute, though, as Pelly Ruddock Mpanzu lost possession under pressure from Smith Rowe, who subsequently sent Kai Havertz away, and the German's ball across the box found Odegaard to fire a crisp, sliced strike into the bottom corner.
Luton responded positively to Arsenal's expected opener, but the Hatters were lacking in attacking firepower and were indebted to Thomas Kaminski for keeping the deficit at just one in the 35th minute, as the 31-year-old denied Smith Rowe from close range.
A few silky turns from the Arsenal men awakened the crowd during the various lulls in action, one of which saw Ben White exquisitely evade Alfie Doughty before slipping in Havertz, but Kaminski was equal to the German's 41st-minute strike from a tight angle.
However, Kaminski was powerless to deny Arsenal their second just three minutes later, as the effervescent Smith Rowe got to the byline on the left-hand side and attempted to pick out Nelson, but his cutback was diverted into the Luton net by Hashioka.
Sloppiness crept into Arsenal's play in the first half of the second period, where David Raya was the busier of the two goalkeepers as Luton sensed a revival, but the Spaniard still had no meaningful save to make.
A few crosses from the Hatters' troops were either thwarted or went awry, but Edwards's men did not lose belief as Arsenal struggled to kick into gear, and nor did their travelling faithful.
Gilt-edged openings continued to elude the visitors, though, and Arsenal came close to wrapping up the win with 10 minutes of normal time remaining through Takehiro Tomiyasu, whose curler from 20 yards bounced just wide of the post.
Fellow substitute Eddie Nketiah then had Kaminski sprawling with an 88th-minute strike from similar range, which would have crept into the bottom corner had it not been for the Belgian goalkeeper, as Arteta's men declared at two.
Now top for at least 24 hours, Arsenal are back in action away to Brighton & Hove Albion on Saturday, while Luton - who stay 18th, three points adrift of safety - host Bournemouth in three days' time.