First-half goals from Lewis Dunk and Glenn Murray secured all three points for the home side, despite Pierre-Emerick Aubameyang halving the deficit before the break.
The result is certain to pile more pressure on Gunners manager Arsene Wenger, who was the subject of angry chants from visiting fans demanding his departure.
Arsenal went into the match on the back of consecutive 3-0 defeats to Manchester City in the EFL Cup final and Premier League, and they found themselves in more trouble when Dunk broke the deadlock seven minutes in.
Murray's header, his sixth goal in 2018, put Brighton two up after a mistake by Laurent Koscielny, prompting an angry response from the travelling supporters.
Aubameyang got a goal back but it was not enough to prevent a fourth defeat in a row in all competitions for the Gunners, marking their worst run since 2002 and leaving them facing a major challenge to finish in the top four.
Arsenal began the match on the front foot but found themselves behind seven minutes in, with Dunk sweeping the ball into the net from 12 yards out after Shane Duffy had beaten Petr Cech to a corner.
The Gunners keeper saved a good Pascal Gross shot as Brighton threatened again, with Dunk and Duffy both heading over from promising positions as the visiting defence failed to deal with routine set-pieces.
With 26 minutes gone, they gifted the home side their second goal. Koscielny's wayward pass was sent out wide to Gross, and his curling cross from the right was headed down and beneath the body of Cech by Murray.
6 - Only Mo Salah (7) and Sergio Aguero (9) have scored more Premier League goals in 2018 than Glenn Murray (6). Mint.— OptaJoe (@OptaJoe) March 4, 2018
'We want Wenger out' was heard loudly from the away end but Aubameyang snatched a lifeline out of nothing two minutes before half-time, flicking Granit Xhaka's strike into the net despite the best efforts of Mat Ryan.
Koscielny almost levelled the match just before the break, rattling the left-hand post with a firm header, and only a flying Ryan save stopped Mesut Ozil blasting home just before the hour mark.
Referee Stuart Attwell made a smart call not to award a penalty when Xhaka went to ground in the area, although Sead Kolasinac was fortunate to escape punishment for a shoulder challenge on Ezequiel Schelotto that ended the Brighton full-back's game.
Wenger threw on Danny Welbeck in the closing stages but there was to be no salvation for the Gunners, who are 13 points adrift of fourth-place Tottenham with just nine matches remaining ahead of their huge Europa League trip to face AC Milan.
Key Opta Stats:
- This was Arsenal's first defeat in 35 Premier League games against promoted sides, since losing 2-1 at QPR in March 2012.
- Arsenal have not kept a clean sheet in their last 11 Premier League games; their joint-longest such run in the competition (also 11 between December and February 2002).
- Pascal Gross has assisted Glenn Murray four times in the Premier League this season – only Cesar Azpilicueta (six for Alvaro Morata) and Kevin De Bruyne (five for Sergio Aguero) have assisted a player more.
- Arsenal have just 13 points from their 15 away Premier League games this season – their worst such return in the top-flight since 1989-90 (12).
- Chris Hughton is only the third manager to beat Arsene Wenger in the Premier League with three different clubs (after Mark Hughes and Sam Allardyce).
- Brighton have won three consecutive Premier League home games for the first time.