The Gunners were famed for their pretty football under long-time manager Arsene Wenger, but Brighton gave them a lesson in the first-half, knitting together some beautiful football that should have resulted in a goal.
New signing Marc Cucurella was dangerous down the right, with Brighton's three centre backs continually wasting golden chances in the area.
Lewis Dunk blasted over from an Aaron Ramsdale spillage that was later given as a foul, while Dan Burn should have easily headed in the opener.
Leandro Trossard and Arsenal's number one enemy Neal Maupay both had a pair of decent chances, coming at the end of some attractive and effective build up play.
The story was the same for much of the second half, only punctured by the odd Arsenal counter which was snuffed out by a confident home team led by the impressive Graham Potter.
The sides ended with two shots on target each when the final whistle, but Brighton can take far more confidence from these two points dropped than from their profligate displays last season.
After a quick start from Arsenal at the rain soaked AmEx, Brighton quickly began to settle in, putting together some football that even Arsene Wenger in his pomp would have been proud of.
New signing from Getafe, Marc Cucurella, was causing the Gunners plenty of problems down the right, before Leandro Trossard faltered with the game's first real chance.
Brighton continued to dominate with the rain clearly affecting goalkeeper Aaron Ramsdale who spilled a cross which Lewis Dunk blasted over from close range, although the whistle soon went for a Shane Duffy push on the keeper after his spillage.
Arsenal had a minor break from the onslaught as Pierre Emerick Aubameyang glanced a header off the post, but the Seagulls fought right back.
Trossard and Neal Maupay both had decent chances before former Seagull Ben White managed to get in the way as Trossard looked set to finish off a beautiful team goal.
6ft 7in Dan Burn missed a sitter of a header just outside the six yard box, with the Seagulls racking up seeming intent on racking up a Premier League record of head-in-hands moments in the first half.
Mikel Arteta's Gunners finished the half with a pair of chances, but it was nothing more than another small bookend to Brighton's 45 minutes of showing Arsenal how to Arsenal.
Brighton started the second half in the same way they ended the first with some nice link up play seeing Jakub Moder curl high and wide.
Arsenal then looked set to take the lead against the run of play with Pierre-Emerick Aubameyang played in one-on-one against Robert Sanchez, and after riding a challenge from the keeper Sean Duffy was there to disrupt and send the shot wide.
Duffy's exceptional last ditch challenge was in vain though, with the initial pass offside.
Brighton continued some more excellent link up play, with Solly Marsh heading down for Maupay to steer in what looked like an easy tap-in, but Ramsdale was there to cut out the pass in commanding fashion.
It looked like Brighton had missed the chance to take the three points with four minutes to play, and that was confirmed when Dunk flashed a header wide from the resulting corner, taking his frustration out on the turf.
Brighton missed the chance to join Chelsea at the Premier League's summit, but Potter will be content with 14 points from seven games.
However, the increasingly highly-rated Englishman will be hoping that this wasn't a rebirth of his wasteful Brighton side from last season, and that the revolution can continue after the international break.