Cole Palmer FC may take some stopping if they can keep this up. While these days it is doing the rest of Enzo Maresca’s side a disservice to ­suggest this is a one-man team, another irresistible performance from the England forward, in which he became the first player in Premier League history to score four times before half-time, made it four wins on the trot for Chelsea.

No wonder that Palmer took the plaudits after a hat-trick in the space of just 10 minutes inspired a sensational response to Chelsea ­falling behind to Georginio Rutter’s early opener after Robert Sánchez’s mistake against his former club. The Chelsea goalkeeper will be mightily relieved that another mistake to allow Carlos Baleba to pull one back did not cause greater damage as Palmer made sure of the points with another brilliant finish before half-time.

Related: Chelsea’s priceless maverick Cole Palmer leaves Brighton all at sea | Barney Ronay

But while Fabian Hürzeler was left aggrieved that his Brighton side were not awarded a penalty at the start of the second half, his somewhat naive insistence of persisting with a high defensive line backfired spectacularly as Chelsea enjoyed their afternoon in the sunshine and moved into the top four. Perhaps Maresca – whose side are now Premier League top scorers after six matches – has found some method among all the madness.

“I just said to Cole, he scored four but he could have scored two or three more,” said Maresca of Palmer’s performance. “It’s good that he continued to be hungry, ambitious. I’ve known Cole for many years because we worked together at Manchester City and the best thing he has is that the way he is today is exactly the same way as he was three or four years ago. Goals, assists – this doesn’t change how he is. He’s a simple guy, a humble guy and that for me is the most important thing.”

Brighton’s fans have clearly not forgotten the fact that Chelsea recruited 11 players and coaches from the south coast club in the 17 months before Maresca’s arrival this summer. The booing of their three former players in Chelsea’s starting lineup began with the first whistle and it did not take long for one of them to give the visiting fans something to cheer.

Sánchez was not entirely to blame after Levi Colwill made a mess of a clearance in only the seventh minute. The Chelsea goalkeeper was left stranded as Rutter was able to head into the empty net. “There’s only one Robert Sánchez,” sang the away end.

But with Hürzeler having insisted he would not deviate from his risky defensive tactics despite the obvious threat posed by Chelsea’s pace on the break, Lewis Dunk and Adam Webster were horribly exposed again and again as Palmer completed his hat-trick in double-quick time.

The England forward had first hit a post before seeing one effort disallowed for offside. But Brighton did not learn their lesson and a poor back-pass from Webster – drafted in for his first start of the season after illness ruled out Jan Paul van Hecke – was seized on by Nicolas Jackson to set up Palmer.

Jadon Sancho thought he had put Chelsea ahead soon after, only for Noni Madueke to be adjudged marginally offside. A desperate challenge from Baleba after Sancho had played a brilliant one-two with Palmer allowed him to sweep home his second from the spot. His third – a superb free-kick into the top corner that left Bart Verbruggen grasping at thin air – came after Pervis Estupiñán had been fortunate not to be sent off for bringing down Jackson. “It was one bad event after another and we couldn’t stop them,” Hürzeler said.

Yet despite Chelsea’s total dominance, Sánchez handed Brighton hope when he inexplicably gifted the ball to Baleba to pull one back. Luckily for him, Palmer was on hand to restore their advantage when he cut in from the left flank and beat Bart Verbruggen at his near post to complete his remarkable achievement just a few months after scoring four against Everton here, including a 16-minute hat-trick.

It appeared that neither manager had instructed his players to calm things down as the second half began in a similarly frantic fashion. Hürzeler was hopping mad after the referee, Peter Bankes, turned down Brighton’s appeals for a penalty for a challenge by Malo Gusto on Kaoru Mitoma that he felt was similar to the one awarded against his side.

• Download the Guardian app from the iOS App Store on iPhone or the Google Play store on Android by searching for 'The Guardian'.

• If you already have the Guardian app, make sure you’re on the most recent version.

• In the Guardian app, tap the Menu button at the bottom right, then go to Settings (the gear icon), then Notifications.

• Turn on sport notifications.

Webster at least partly redeemed himself when he cleared Jackson’s shot off the line after more confusion in the Brighton defence but it seemed inevitable that Chelsea would score again when Palmer volleyed just over from distance before firing wide when clean through again.

Webster was finally put out of his misery after that and the afternoon would have got worse for Brighton had Marc Cucurella’s volley from a corner not been ruled out for offside.