Substitute Jeff Hendrick fired in a stoppage-time equaliser to earn Burnley a point and deny Brighton their first home victory since 2 March.
The Seagulls were set to win it when Neal Maupay volleyed in Solly March’s cross at the start of the second half.
The summer signing struck after March and Glenn Murray tested Burnley keeper Nick Pope just before the break.
But Hendrick drilled in a 20-yard strike to keep both sides looking for their first win since the opening day.
The 27-year-old midfielder, who won his 50th cap for the Republic of Ireland in midweek, came off the bench for his 100th Premier League appearance and salvaged a point for the Clarets with their first shot on target.
The visitors had started stronger, with Jack Cork and Aaron Lennon having shots blocked, before Brighton finished the first half on top.
After Maupay’s second goal for the club since his £16m move from Brentford, Davy Propper spurned a good chance to double the lead as he headed over from Murray’s cut-back before the veteran English forward also skewed a 20-yard effort well wide.
And Hendrick made them pay, 12 seconds into the four minutes of added time, to keep the two sides level in the Premier League table on five points.
Potter still waiting for first home win
After narrowly avoiding relegation last season, Brighton have been more expansive under new manager Graham Potter and took four points from their first two games.
And despite then losing to Southampton and Manchester City, the Seagulls looked comfortable against their south coast rivals until Florin Andone’s red card and were more adventurous than most teams at Etihad Stadium, having 46.5% possession and creating chances of their own.
Back at the Amex, they took time to get a foothold in the game before putting together some positive build-up play.
Initially, March was their biggest outlet on the left. He even popped up on the right wing to whip in a teasing cross which Murray glanced beyond the far post.
Pascal Gross also got into some promising positions down the right channel, without picking out a team-mate in the middle, and that expansive play continued after the break.
Burnley defender Matt Lowton deflected Murray’s cut-back just wide while Maupay tested Pope at his near post before swivelling to fire in the opener.
Shane Duffy returned for Brighton and despite facing in-form striker Ashley Barnes and his partner Chris Wood – so often the scourge of Albion since helping them win the League One title in 2010-11 – the Seagulls’ defence kept Burnley’s front two quiet.
They only had one chance to equalise which Wood, who scored twice in the Clarets’ win here last season, sidefooted wide from close range before Brighton’s late lapse cost Potter his first win.
Clarets clinical at the death
Burnley’s opening-day win over Southampton had Clarets fans dreaming of another top-seven finish after qualifying for last season’s Europa League and it took a stoppage-time penalty to deny them another victory at Wolves.
Manager Sean Dyche was happy with his side’s performance in defeat at Arsenal and they matched Liverpool until two goals late in the first half set the European champions on course for a 3-0 win last time out.
The Clarets again started positively, with Dwight McNeil winning a string of corners down the left wing, but were firmly on the back foot after Lennon went close on 37 minutes.
They were stretched by the hosts and despite Barnes’ best efforts up front, a chance never fell for the striker to add to his four goals so far this season.
Wood had one of his off days yet, just as Burnley looked set to return from the south coast empty handed, they showed the quality they possess by pouncing when the opportunity arose.
With Brighton adjusting to a substitution moments earlier, McNeil ran at the home defence before playing it into Matej Vydra, who laid off for fellow sub Hendrick to hit a crisp first-time strike which veered away from keeper Mat Ryan into the bottom corner.
More to follow.