Brighton were made to rue a number of missed opportunities as David Ngog's last-gasp strike earned Bolton an unlikely 1-1 draw at the Amex Stadium.
The former Liverpool striker netted with the last kick of the game to cancel out Bruno Saltor's opener and preserve Dougie Freedman's unbeaten record as Bolton boss.
The hosts dominated from the off and should have been out of sight at half-time, but Ashley Barnes failed to mark his 100th Brighton start with a goal as he missed a penalty.
The woodwork also came to the Trotters' rescue, with Andrea Orlandi, Dean Hammond and Craig Mackail-Smith all denied.
Brighton were awarded a penalty in the 14th minute when Darren Pratley was harshly adjudged to have handled Mackail-Smith's cross in the box.
However, Barnes saw his spot-kick well saved by Adam Bogdan, who then superbly blocked the four-goal striker's rebound. The hosts went close again when Orlandi and Hammond both had shots cannon back off the crossbar in quick succession.
Poyet's troops continued their dominance and Bogdan had to dive to his left to deny the lively Mackail-Smith before the bar stopped the striker's header from going in after 35 minutes.
The Trotters came out with more purpose after the interval, with Ngog shooting over from 20 yards, and they were aggrieved not to be given a penalty of their own when the ball looked to have hit Marcos Painter's arm in the box.
However, Brighton finally opened the scoring in the 54th minute. Mackail-Smith was brought down by Matt Mills and after Orlandi's free-kick was cleared to the edge of the box, Bruno fired into the bottom corner from 30 yards.
Orlandi almost doubled his team's advantage, testing Bogdan before seeing an effort shave the post after he did well to create some space.
Will Hoskins almost made the points safe, only to see Bogdan dive to his left and tip the substitute's effort round the post.
But Bolton punished Brighton's failure to convert when Ngog found the bottom corner from eight yards five minutes into stoppage time.