Premier League: The Seagulls seem destined for an unfortunate defeat after Conor Gallagher's seventh goal of the season gave Palace a 69th-minute lead against the run of play.
Leandro Trossard, Danny Welbeck and Neal Maupay were on target for Brighton as for once this season Graham Potter's men turned their dominance into goals.
Arsenal's hopes of qualifying for the Champions League suffered a fatal blow as Neal Maupay fired Brighton to a last-gasp 2-1 win, while Watford snatched a late 1-1 draw against Leicester.