After a goalless first-half, the Hatters went ahead when Sam Parkin hit his fifth of the season - and fourth in his last six games - in the 49th minute.
But the Seagulls responded within seconds to level through Ian Westlake's first of the season, before Glenn Murray's 59th winner sealed Luton's fate.
The game kicked off with the floodlights on despite the pitch being bathed in bright sunshine and Paul McVeigh almost lit up proceedings further with a 20-yard volley straight at Michel Kuipers in the third minute.
Westlake responded for the visitors by firing into the side-netting following Keith Keane's misdirected header after a sixth minute Murray flick-on.
Westlake then repeated the trick three minutes later when he really should have hit the target after Luton goalkeeper Dean Brill had palmed Murray's cross-shot into his path.
In an all-action start, Don Hutchison then went close for the Hatters by powering an eight-yard header at Kuipers after McVeigh's 11th minute corner.
The game settled down until visiting goalkeeper Kuipers comfortably held a 20-yard Parkin curler in the 25th minute.
Four minutes later, Brill had to save at full stretch from his own defender Sol Davis after Dean Cox's dangerous free-kick into the box for Brighton.
The best chance of the half came two minutes before the break when Ed Asafa-Adjaye curled a superb cross into the box for the hosts, but Parkin put his eight-yard header wide.
Four minutes after the break, Luton went ahead when Jonny Dixon was penalised for a needless shove on Lewis Emanuel, allowing Davis to pump in a free-kick which was chested down by Calvin Andrew for Parkin to round Kuipers and score.
The lead lasted just 30 seconds though as Brighton advanced from the restart to eventually see Cox cross from the right for Westlake to find the net off the underside of the crossbar with a looping far-post header.
In the 59th minute it was 2-1 to the visitors with Cox again the provider from the right allowing Murray to firmly head past Brill from six yards for his sixth of the campaign.
Andrew had a great chance to level for Luton when his turn took him clear in the 70th minute, but Kuipers produced a point-blank save.
Brill matched Kuipers' heroics five minutes later by blocking Steve Thomson's close-range drive to prevent Brighton stretching their lead.