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It was a controversial climax to an eventful derby on the South Coast as Palace came from behind twice to gain revenge for Brighton's 1-0 win at Selhurst Park last month.
Brighton went ahead in the 22nd minute with Leon Knight's fourth goal of the season.
A misplaced pass by Tom Soares gifted possession to Alex Frutos and his cross to the near post was flicked in by Knight from close range.
It was the perfect way for Knight to celebrate his return to the team. He was dropped for Brighton's previous match at Stoke because manager Mark McGhee was unhappy with the way he reacted to being substituted in the home game against Wolves.
Brighton's lead lasted only six minutes, the unmarked Dougie Freedman heading his 100th goal for Palace from a left-wing cross by strike partner Clinton Morrison.
Brighton regained the advantage in the 53rd minute. Jake Robinson was impeded inside the box by Palace defender Gary Borrowdale as he tried to latch on to a ball from Dean Hammond.
Referee Nick Fletcher missed the incident but he awarded a penalty on the advice of his assistant. Knight's spot-kick squirmed past the diving Gabor Kiraly.
The Seagulls' lead was again short lived as Palace levelled on the hour with a fine finish by Freedman.
He controlled a cross from Marco Reich and made room for himself to fire an angled drive into the far corner.
The match turned against Brighton in the closing stages when Hart, booked in the 84th minute for a foul on McAnuff, received a second caution for deliberate handball three minutes later while receiving treatment off the pitch.
Hart was eventually stretchered away and his and Brighton's agony was compounded when Freedman set up McAnuff to drill in a low right-foot drive from 20 yards.
Palace's dramatic victory lifts them three places to ninth in the Championship table, while Brighton remain second from bottom.
It was a controversial climax to an eventful derby on the South Coast as Palace came from behind twice to gain revenge for Brighton's 1-0 win at Selhurst Park last month.
Brighton went ahead in the 22nd minute with Leon Knight's fourth goal of the season.
A misplaced pass by Tom Soares gifted possession to Alex Frutos and his cross to the near post was flicked in by Knight from close range.
It was the perfect way for Knight to celebrate his return to the team. He was dropped for Brighton's previous match at Stoke because manager Mark McGhee was unhappy with the way he reacted to being substituted in the home game against Wolves.
Brighton's lead lasted only six minutes, the unmarked Dougie Freedman heading his 100th goal for Palace from a left-wing cross by strike partner Clinton Morrison.
Brighton regained the advantage in the 53rd minute. Jake Robinson was impeded inside the box by Palace defender Gary Borrowdale as he tried to latch on to a ball from Dean Hammond.
Referee Nick Fletcher missed the incident but he awarded a penalty on the advice of his assistant. Knight's spot-kick squirmed past the diving Gabor Kiraly.
The Seagulls' lead was again short lived as Palace levelled on the hour with a fine finish by Freedman.
He controlled a cross from Marco Reich and made room for himself to fire an angled drive into the far corner.
The match turned against Brighton in the closing stages when Hart, booked in the 84th minute for a foul on McAnuff, received a second caution for deliberate handball three minutes later while receiving treatment off the pitch.
Hart was eventually stretchered away and his and Brighton's agony was compounded when Freedman set up McAnuff to drill in a low right-foot drive from 20 yards.
Palace's dramatic victory lifts them three places to ninth in the Championship table, while Brighton remain second from bottom.