Pierre-Emerick Aubameyang gave Unai Emery's men an early lead from the penalty spot, but Brighton - whose survival was rubbed-stamped by Cardiff City's relegation on Saturday - battled back to claim a deserved draw.
Glenn Murray converted another penalty and the battle for the last Champions League place will now be fought by Tottenham and Arsenal on the final day of the season, though fourth-placed Spurs have a three-point cushion and a huge advantage over their north London rivals on goal difference.
Henrikh Mkhitaryan's 20-yard drive hit the foot of the post as Arsenal started well, with the Gunners taking the lead in the ninth minute from the penalty spot.
Nacho Monreal went down under Alireza Jahanbakhsh's clumsy challenge and Aubameyang sent Mat Ryan the wrong way for his 20th Premier League goal of the season.
After sustained Brighton pressure - led by Yves Bissouma's persistence - the Arsenal goalkeeper Bernd Leno claimed Murray's header while Lucas Torreira rifled wide at the other end.
Solly March stung Leno's palms after the restart and the visitors drew level on the hour from the penalty spot after the Brighton winger was tripped by Granit Xhaka.
Murray coolly converted, beating Leno easily to score his first Premier League goal since March, with Aubameyang missing a fantastic chance to restore Arsenal's lead in the 74th minute.
Emery made a triple change in a desperate late throw of the dice but his side could not find another goal, with their hopes of playing in next season's Champions League now likely dependent on them winning the Europa League.
And Brighton should have wrapped up the top-four situation with five minutes left when March's header was blocked by Leno, Pascal Gross horribly firing the rebound well off target.
What does it mean? Nervy finale for top-four race
Teams continue to slip up in the battle to secure Champions League qualification, with Arsenal unable to take advantage of nine-man Spurs losing 1-0 at Bournemouth on Saturday.
With both teams in European semi-finals in midweek, there will be some tired legs next weekend when the campaign comes to a conclusion, although it would need to be a remarkable pair of results to see Arsenal pip Spurs, who host Everton.
Bissouma flies high for Seagulls
Few have impressed for Brighton in a poor second half of the campaign, but Chris Hughton has a solid foundation on which he can build in the form of midfielder Bissouma.
His ball-carrying skills repeatedly unnerved the Arsenal back line, while the Mali international also showed the combative side of his game by competing in an impressive 19 duels.
Xhaka the fall guy again
Both penalties were arguably harsh decisions from referee Anthony Taylor, but Xhaka continues to find himself on the scene of crimes seemingly more often than not when things go wrong for Arsenal.
50 - Arsenal have conceded at least 50 goals in consecutive top-flight campaigns for the first time since 1982-83/1983-84. Trouble. #ARSBHA— OptaJoe (@OptaJoe) May 5, 2019
Key Opta Facts
- Arsenal are winless in their last four Premier League games (D1 L3), their longest run without a victory in the competition since February 2016 (also four games).
- Arsenal failed to win both league meetings against Brighton this season (D2), despite opening the scoring in both games – they last did this against an opponent in a Premier League campaign in 2010-11 v Spurs (D1 L1).
- Brighton avoided defeat away from home against 'big-six' opposition for the first time in the Premier League – they had lost each of their last 11 games before today.
- Aubameyang is the sixth different player to score 20-plus goals in a Premier League season for the club, and the first since Alexis Sanchez in 2016-17.
- Since making his debut in the competition in February 2018, only Mohamed Salah (35) has scored more Premier League goals than Aubameyang (30).
Arsenal travel to Valencia for the second leg of the Europa League semi-final on Thursday - in a tie they are 3-1 up in after the first leg - before heading to Burnley to wrap up their Premier League campaign three days later. Brighton finish their season at home to Manchester City in a match that could decide who wins the title.