The Blues were looking for their fourth win in a row in all competitions after beating Barrow 5-0 in the Carabao Cup.
Palmer was superb in the game, scoring four goals in the first 40 minutes of the first half in their 4-2 victory.
The Chelsea star becomes the first player in the history of the Premier League to score four goals in a first-half game.
As it happened
Chelsea made just one change from the side that beat West Ham last weekend as Malo Gusto comes back into the defence in place of Tosin Adarabioyo.
Brighton made three changes from the team that played Forest, with Adam Webster, Ferdi Kadioglu and Mats Wieffer replacing Simon Adingra, Jan Paul Van Hecke and Joel Veltman.
The game started with Brighton looking threatening and their threat paid off in the first 10 minutes of the game.
Moises Caicedo and Levi Colwill are both involved and then keeper Robert Sanchez rushes off his line - with Georginio Rutter heading the ball above him into an empty net.
Cole Palmer was in top form, scoring the first three goals to put Chelsea in front in the first 30 minutes.
Brighton reduced the deficit to just one, but Chelsea pushed forward again and a mistake from the Brighton backline gave Palmer his fourth goal of the game in just 40 minutes.
The second half did not produce much, but Chelsea still produced a goal that was disallowed for offside.
The game ended in a comfortable win for Chelsea as they sealed a 4-2 win over Wolves at Stamford Bridge.