The Gunners needed to respond after City's 3-0 win over Everton earlier on Sunday left Mikel Arteta's side trailing by four points in the race for the title.
On a deeply frustrating day for Arsenal, Leandro Trossard hit the bar against his former club while Martin Odegaard and Bukayo Saka both went close before Julio Enciso's close-range header put Brighton ahead.
Substitute Deniz Undav doubled the lead after lobbing Aaron Ramsdale in the 86th minute before Pervis Estupinan added to Arsenal's misery with Brighton's third in the 96th minute.
City will win the Premier League title next Sunday in front of their own fans if they beat Chelsea at home (16:00 BST), even if Arsenal defeat Nottingham Forest at the City Ground on Saturday (17:30).
However, City will be confirmed champions without playing on Saturday if the Gunners lose at Forest.
In a game littered with niggly challenges, Arsenal lost Brazil forward Gabriel Martinelli to injury in the first half after a foul by Brighton's Ecuador midfielder Moises Caicedo, who the Gunners tried to sign in January.
Brighton, who are chasing a place in Europe for the first time, had gone close through Enciso before the 19-year-old Paraguay forward stunned the Emirates with his 51st-minute goal.
The win lifted the Seagulls above both Aston Villa and Tottenham into sixth on 58 points, four behind fifth-placed Liverpool with one game in hand.
The maximum number of points Arsenal can score is 87, while City have 85 with matches against Chelsea (home), Brighton (away) and Brentford (away) to come.
Arsenal's players sank to their knees after the full-time whistle, the realisation quickly sinking in that their title dream was all but over after being picked off by Brighton.
The Gunners deserve enormous credit for the way they have pushed Manchester City in the title race. They were eight points clear of City at the top after 18 games but their pursuit is running out of steam after a highly damaging defeat at the business end of the season.
Manchester City's comfortable win at Everton earlier on Sunday opened up a four-point gap at the top but this time Arsenal were unable to respond to the pressure heaped on them by Pep Guardiola's Treble-chasing team.
There was still almost 40 minutes left when Enciso opened the scoring and Arteta sent on Eddie Nketiah and Emile Smith Rowe to try and salvage a point.
But the Arsenal boss, who was shown a yellow card by referee Andy Madley, saw his side concede two further goals while the home side failed to score for the first time since 4 February on their way to a comprehensive defeat.
"We knew the challenge we had, it was very different to the one we had at Newcastle," Arteta told Match of the Day, referencing a 2-0 win.
"I was stood here and very proud of what we did last week but today we have to apologise to our people. We have to move on very quickly and not keep that feeling for a long time."
This was another statement win in what looks like being a history-defining season for Brighton, who bounced back from a crushing 5-1 home defeat by Everton to produce one of their best performances of the season.
They were at their clinical best as Arsenal were beaten at the Emirates for only the second time in the league.
Roberto De Zerbi has called on his players to "write club history" by qualifying for Europe for the first time.
"It's not enough to qualify for the Europa League," said De Zerbi. "We have four games and they're all tough games. We have 58 points and that's not enough. We have to win other games and the first game will be in Newcastle [on Thursday].
"I enjoy working with the players. I am very lucky to be their coach and I am happy they enjoy working with me.
"That's a great satisfaction for me, but I prefer to speak about everything at the end of the season because we want to achieve something historic for the fans and for the club."
Two wins from the last four games - Newcastle (away), Southampton (home), Manchester City (home), Aston Villa (away) - will be enough to see the Seagulls confirm their place in next season's Europa League.
Against Arsenal, Brighton were at their attacking best, registering six chances on target and scoring from half of them.
"The manager showed us a Michael Jordan video, to show us how he motivated himself for each game," goalscorer Undav told Sky Sports.
"It was the right choice to show us the video and we showed today how mentally strong we are."
As Arsenal's players looked desolate at the final whistle, Brighton's triumphantly marched over to where their travelling fans were gathered to show their appreciation.
This incredible season for the Seagulls, which has included an FA Cup semi-final and league doubles over Manchester United and Chelsea, is far from over.