Glenn Murray scored a controversial penalty to put Brighton ahead and the hosts added another two after Shane Duffy was dismissed for pushing his head into Patrick van Aanholt's in the 28th minute.
The red card prompted the introduction of Leon Balogun and he netted with his first touch, while Florin Andone, who came on after Murray sustained a shoulder injury, struck for the second match in succession just before the break.
Luka Milivojevic converted from the spot nine minutes from time, but Palace were unable to avoid slipping to a disheartening defeat after a promising draw at Manchester United and win at Burnley in their previous outings.
The visitors were unfortunate to fall behind in the 24th minute when referee Kevin Friend deemed that James McArthur had fouled Jose Izquierdo despite winning the ball and Murray guided the resultant penalty home.
Friend did not award a spot-kick when James Tomkins sent Murray to ground and while the striker received treatment on his shoulder Duffy was shown a red card for a clash with Van Aanholt.
Chris Hughton sent Balogun on in response and the Nigeria international lashed a brilliant right-footed strike past Wayne Hennessey just 25 seconds later to complete a remarkable string of events.
Murray had to be replaced by Andone and, after a brilliant goal-line clearance from Bernardo kept Milivojevic out, the Romanian punished Palace on the counter-attack in the fourth minute of stoppage time.
Brighton tried to hold out for a fourth Premier League clean sheet of the season but were unable to do so as Milivojevic scored a penalty for Palace after Wilfried Zaha was fouled by Balogun, though it was nothing but a consolation.
What does it mean? Brighton's resilience shines through
Brighton showed great character in responding to conceding a first-minute goal at 10-man Huddersfield Town on Saturday by going on to win 2-1. This time it was the Seagulls who were at a numerical disadvantage and still managed to complete an incredible over their rivals. The fact that two of their goals came while they were a man light and were not scored by Murray will be a huge boost for Hughton.
Andone brushes off being dropped
Murray returned to the starting line-up after being rested against Huddersfield and Andone's winner at the John Smith's Stadium may have made Hughton's decision tough to take. However, the 25-year-old was the epitome of professionalism as he chased after every ball. It was key for his first-half goal and kept Palace on their toes as the hosts sat back after the interval.
Milestone man Zaha goes missing
In his 300th Palace appearance, Zaha was up against the side he has scored more goals versus than any other. The Ivory Coast international created the opening that Milivojevic saw blocked by Bernardo but contributed little else in a dismal performance from Roy Hodgson's side. Winning a penalty nine minutes from time was too little, too late.
Key Opta Facts
- Brighton and Hove Albion's 3-1 win over Crystal Palace is their first victory in a midweek Premier League match (Tuesday, Wednesday, Thursday), drawing three and losing three of the previous six.
- Palace have picked up just one point from their last five Premier League away games (D1 L4), scoring three goals and conceding 10.
- Brighton have lost just one of their last 10 Premier League games at the Amex Stadium (W5 D4), winning three of their last four (D1).
- Seagulls striker Glenn Murray has scored the opening goal in five Premier League games this season – only Mohamed Salah (6) has done so in more.
- Palace's Wilfried Zaha has won more penalties (7) and Luka Milivojevic has scored more penalties (10) than any other player in the Premier League since last season.
Another derby is on the horizon for Palace – they will cross London to take on West Ham at London Stadium on Saturday. Brighton will take on Burnley at Turf Moor on the same day.