Brighton 1 Chelsea 2 - Highlights
Chelsea just need a point to secure European football next season after a win at Brighton
Cole Palmer put Chelsea ahead with the 22nd league goal of his superb season in the 34th minute.
Ignoring the boos from the stands, former Brighton left-back Marc Cucurella chipped his cross towards Palmer, who looped a clinical header past Bart Verbruggen.
Christopher Nkunku doubled Chelsea's advantage in the 64th minute with his third league goal of an injury-plagued first season with the club.
Nkunku finished off Malo Gusto's cross to leave Brighton deflated and celebrated by blowing up a blue balloon lying on the pitch.
Chelsea defender Reece James was sent off in the 88th minute for kicking Joao Pedro after being knocked over by the Brighton striker.
Danny Welbeck's close-range finish in the seventh minute of stoppage-time came too late to stop Chelsea recording four successive league wins for the first time since October 2022.
Mauricio Pochettino's side host Bournemouth on Sunday knowing a draw will be enough to earn a European berth, with fifth place still in play if they win and Tottenham lose at Sheffield United.