A team built on a water-tight defence, it was the first time the Gunners had conceded three goals in a league encounter in more than three years.
Mikel Arteta's charges had come into the contest on the back of four consecutive league wins to start the season, but fell flat as the Seagulls turned them over comfortably.
The home side themselves have had a decent start to the campaign and they rallied to conjure up their third victory in five league matches, while they also knocked Manchester United out of the Carabao Cup on Wednesday.
That confidence was seen in the opening exchanges and Brighton took the lead just after the half-hour mark when Pascal Gross struck a low-range effort that beat goalkeeper David Raya.
Arsenal then had a gilt-edge opportunity to equalise but Bukayo Saka could not finish from close-range and, from the counter-attack, Charalampos Kostoulas made it 2-0 with another long shot.
The defending champions needed something special if they were to launch a comeback in the second half but it got worse when Chema Andres found himself unmarked from a corner and headed in to make it 3-0 in the 57th minute.
Arsenal were stunned and had few half chances to get back into the contest but it was to no avail as Brighton scored three goals and wrapped up the three points.
Enzo Maresca has admitted he would have preferred a routine 1-0 victory after Manchester City survived a huge scare to beat Sunderland 5-3 in a thrilling Premier League encounter on Sunday.
Michael Carrick has insisted Manchester United can take positives from their 1-1 draw at Fulham despite another disappointing result in the Premier League.
Liverpool manager Andoni Iraola has challenged Alexander Isak to raise his level after the striker scored the goal that secured a hard-fought 1-0 Premier League win at Bournemouth on Sunday.
Manchester City edged Sunderland 5-3 in arguably the most entertaining match of the Premier League season so far at the Etihad on Sunday afternoon.
