Spurs boss Thomas Frank shuffled his pack after his side were in midweek action, and one of the players he brought into the starting XI, Destiny Udogie, was in the thick of the action early on.
He found space down the left and squared for Lucas Bergvall, but Jan Paul van Hecke stole ahead of the midfielder to clear the danger.
That intervention looked even more vital on eight minutes when the Seagulls hit the front against the run of play.
Yankuba Minteh beat the offside trap and raced through on goal from Georginio Rutter’s ball, showing tremendous composure to round Guglielmo Vicario and slot home his second goal in as many meetings on this ground.
Brighton were unbeaten in all six previous games Minteh had scored in for them, and after Richarlison and Wilson Odobert missed the target, the hosts looked set to continue that streak as they doubled their lead.
Bergvall was caught in possession in his own third, allowing Yasin Ayari to punish him, curling in from long range with the swerve on his shot, perplexing Vicario, who really ought to have done better.
The scoreline was harsh on Tottenham, who were the better side for large periods of the first half, and they deservedly reduced the arrears just before half-time through Richarlison, who settled Mohammed Kudus’ shot and stabbed home from close range.
Concerted Tottenham pressure following the restart ultimately came to nothing, prompting the introduction of new signing Xavi Simons from the bench.
He was charged with bucking a trend that had seen nine of Spurs’ last 12 matches have the half-time result replicated at the final whistle, but that task nearly became much harder when Ayari’s long-range strike whistled just wide of the target.
Having survived that scare, Simons began to work his magic, weaving his way to the edge of the box where he saw a shot well saved by Bart Verbruggen, before he dragged another effort wide of the target.
Spurs’ pressure was relentless at times, and as the game entered the final 10 minutes, they finally got an equaliser.
Having been found by Simons, Kudus’ inviting cross from the right was inadvertently deflected into the bottom corner by Van Hecke, prompting delirium in the away end with plenty of time still to chase a winner.
Unfortunately for the visitors, Brighton composed themselves from there to hang on to a draw, but squandering the lead leaves the Seagulls with just five points from as many games, while Spurs are unbeaten in three away league games under Thomas Frank.
Flashscore Man of the Match: Xavi Simons (Tottenham Hotspur)