Calvin Andrew headed home a 90th minute winner after fellow capture Seb Carole came off the bench to set up Nicky Forster's second-half equaliser.
Andrew was signed this week on loan from Crystal Palace for the rest of the season.
French winger Carole is at Brighton following a successful trial after playing for them three years ago when they were relegated from the Championship.
Boss Micky Adams introduced Carole for Chris Birchall 11 minutes into the second half.
The decision was not particularly popular with the fans, who felt Birchall deserved to stay on.
But it paid immediate dividends when Dean Cox crossed to the far post and Carole volleyed into the danger area for Forster to knock in his 12th goal of the season from point-blank range.
Adams made another key substitution, bringing off Cox and introducing Kevin McLeod on the left wing.
It was McLeod who supplied the cross for Andrew to nod Brighton's last-gasp winner into the roof of the net at the near post.
Hartlepool had taken the lead in the 19th minute when Australian striker Joel Porter got to the byline and crossed for captain Michael Nelson to volley in from close range.
Daniel Nardiello, making his debut on loan from Blackpool, should have doubled their lead early in the second half but volleyed over from 10 yards.
Nardiello had strong claims for a penalty rejected by referee Dean Whitestone five minutes later.
He got away from Tommy Elphick and the Brighton defender seemed to drag him down.
Keeper John Sullivan was in good form for Brighton, saving twice from Matty Robson in the second half to lay the foundations for Brighton's comeback.