It seemed like a disappointing afternoon for Brighton, who dominated the game but could not find an answer to Wilfried Zaha’s 19th-minute penalty for the hosts.
After Tariq Lamptey was ruled to beat Michy Batshuayi in the area when the cross was playing, Zaha fired past Brighton goaltender Matt Ryan for his fourth goal of the season.
Brighton overtook Palace and scored a total of 20 goals against Palace’s, but they had to wait until the 90th minute when Argentina’s Mac Allister was propelled by a deflected ball.
However, Brighton finished the game with 10 men, after Lewis Dunk had been sent off for a bad battle against Gary Cahill at the time of the stoppage.
Palace has seven points and is in 12th place, with Brighton three points worse off in 16th place, having suffered consecutive defeats after winning the first two games.