The Blues had trailed early on as Georginio Rutter took advantage of a calamity of errors in the Chelsea defence to head in his first goal for the Seagulls.
However, Palmer soon took over to become the first Premier League player to score four times in the first half.
The England international swept home Nicolas Jackson’s pass to level before he coolly slotted in from the penalty spot.
Palmer completed his third Chelsea hat-trick in style with a free-kick that curled into the top corner.
