A quite stunning first half at Stamford Bridge produced six goals, with four of those coming from Palmer, who has proven to be a sensational signing for the capital giants.
The breakthrough arrived in the seventh minute, with Georginio Rutter sending Brighton ahead after poor defensive work from Chelsea, heading into the back of the net to silence Stamford Bridge.
However, it was 1-1 in the 21st minute when Palmer converted after smart work from Nicolas Jackson, and he then scored twice more in quick succession, registering from the penalty spot after Jadon Sancho was fouled inside the box, and firing an excellent free kick into the top corner.
Brighton were back in the match in the 34th minute, with Carlos Baleba converting after a mistake from Chelsea goalkeeper Robert Sanchez, but Palmer was at it again in the latter stages of the first period, squeezing the ball home at the far post after a mistake from Brighton stopper Bart Verbruggen.
It was not a surprise that the second half was a lot quieter after a stunning first period, and Brighton were unable to find a route back into the contest, with Enzo Maresca's side making it four wins from their opening six league matches, and they are also now the leading goalscorers in the division this term with 15.
The victory has moved Chelsea into third position in the Premier League table, boasting 13 points from their opening six matches, and they are now just one point off leaders Manchester City.
Brighton, meanwhile, have dropped into eighth spot, with the Seagulls on nine points from six matches, as they suffered their first defeat of the campaign in spectacular circumstances.
CHELSEA VS. BRIGHTON HIGHLIGHTS
7th min: Chelsea 0-1 Brighton (Georginio Rutter)
Brighton take the lead in the seventh minute of the match, with Ruttner heading into the back of the net from inside the box after poor defending from Chelsea. The Seagulls are ahead at Stamford Bridge!
21st min: Chelsea 1-1 Brighton (Cole Palmer)
Chelsea level the scores in the 21st minute of the contest, and it is Palmer with the goal; the Englishman is found by Jackson, and he makes no mistake to level the scores.
28th min: Chelsea 2-1 Brighton (Cole Palmer)
Chelsea take a 2-1 lead in the 28th minute of the clash in London, with Palmer expertly finding the bottom corner from the penalty spot after Sancho is fouled inside the box.
31st min: Chelsea 3-1 Brighton (Cole Palmer)
Palmer his a first-half hat trick in the English capital, as the Englishman finds the back of the net from a brilliant free kick. The former Manchester City youngster picked out the top corner from distance.
34th min: Chelsea 3-2 Brighton (Carlos Baleba)
Brighton get themselves back in the match at Stamford Bridge, as Baleba finds the back of the net following more poor defensive work from Chelsea, with goalkeeper Sanchez giving the ball away.
41st min: Chelsea 4-2 Brighton (Cole Palmer)
Incredible scenes here - Palmer his fourth in the first half of this match, firing into the bottom corner after another defensive mistake, with Seagulls goalkeeper Verbruggen giving the ball away in a dangerous area.
Palmer has become the first player in Premier League history to score four goals before half-time in a single game. What an opening 45 minutes from the England international.
MAN OF THE MATCH - COLE PALMER
Few would have predicted the impact that Palmer has had at Chelsea, and Manchester City surely must regret allowing the forward to leave in the summer of 2023.
Palmer has now managed six goals and four assists in eight appearances in all competitions this season, and he has simply sensational against Brighton in the opening half of action.
The 22-year-old had seven shots in total, and he might have had a couple of assists in the second period, but Chelsea passed up a number of opportunities to add to their total for the afternoon.
CHELSEA VS. BRIGHTON MATCH STATS
Possession: Chelsea 40%-60% Brighton
Shots: Chelsea 14-15 Brighton
Shots on target: Chelsea 5-5 Brighton
Corners: Chelsea 8-2 Brighton
Fouls: Chelsea 11-9 Brighton
BEST STATS
WHAT NEXT?
Chelsea will be aiming to make it five straight wins in all competitions when they welcome Gent to Stamford Bridge in the Conference League on Thursday night; the Blues will then resume their Premier League campaign at home to Nottingham Forest next Sunday.
Brighton, meanwhile, will be bidding to bounce back from the defeat when they welcome Tottenham Hotspur to the Amex next weekend.