They beat Tottenham Hotspur 4-3 in a frenzied London derby at Tottenham Hotspur Stadium, and closed the gap with Premier League leaders Liverpool this morning.
Two comical slips by Chelsea full back Marc Cucurella led to Dominic Solanke and Dejan Kulusevski giving the hosts a dream start. But their joy turned to despair as the visitors showed why they should be considered title contenders.
Jadon Sancho rifled in a shot after 17 minutes to give Chelsea momentum and Palmer equalised from the spot just past the hour mark as Chelsea dominated the second period.
Enzo Fernandez powered home a shot to put Chelsea ahead and Palmer effectively wrapped it up with his second penalty late on, before Son Heung-min scored a stoppage-time consolation goal.
Chelsea are in second place with 31 points from 15 games, four points behind Liverpool, who game have a game in hand after their match against Everton was postponed because of high winds.
Tottenham's second defeat of the week left them in 11th place with 20 points and the pressure mounting on manager Ange Postecoglou, whose cause was not helped by losing centre back Cristian Romero to injury early on.
"It's a sore one for sure, it's painful. We started the game really well and then we lose Cristian Romero and we had to reshuffle," the Australian, whose side have twice lost having led 2-0 this season, told Sky Sports.
"The momentum shifted pretty quickly."
Chelsea manager Enzo Maresca has played down the title chances of his expensively-assembled squad who are now unbeaten in seven games and have won their last four Premier League matches. They are also top scorers in the division with 35 goals and in Palmer have a player at the peak of his powers.
He now has 50 goal involvements (33 goals and 17 assists) in 48 Premier League games for the London club since joining from Manchester City.
"The first 10 or 15 minutes we conceded two easy goals but overall we were in control of the game," Italian Maresca said. "The reaction of the players was mentally strong both on and off the ball."
Things looked bleak for the visitors early on as a tumbling Cucurella was twice left red-faced.
He lost his footing in the fifth minute and Brennan Johnson played the ball into the area when Solanke produced a poacher's finish to give his side the lead.
Minutes later the exact same thing happened, this time the Spaniard slipping over and looking on in horror as the ball was eventually played to Kulusevski who cut across the area before threading a precise shot past Emiliano Sanchez.
Cucurella went off to change his footwear and his side's fortunes quickly changed too, Sancho striking a wonderful shot in off the post after a surging diagonal run.
Chelsea were perhaps lucky not to be down to 10 men when Moises Caicedo followed through on Pape Matar Sarr and soon afterwards Sarr headed a cross against the woodwork.
Tottenham were hanging on to their lead in the second half but a reckless challenge by Yves Bissouma on Caicedo was a clear penalty and Palmer beat Fraser Forster.
The hosts briefly rallied with Son going close but Fernandez volleyed Chelsea in front in the 73rd minute after a mazy dribble by the unstoppable Palmer.
Palmer then capped a great afternoon when he was brought down by Sarr and delivered an audacious 'Panenka' penalty.
Son's tap-in was scant consolation for Tottenham who also lost Romero's defensive partner Micky van de Ven to injury near the end.
Arsenal held to draw
Meanwhile in West London Arsenal were held to a 1-1 draw by Fulham, on a grey wet day at Craven Cottage.
Raul Jimenez scored early for the hosts and William Saliba equalised for the visitors at the start of the second half.
The result leaves Arsenal third on the table on 29 points, two ahead of Manchester City, following the defending champions' draw against Fulham.
Fulham, who also thwarted the Gunners both home and away last season, have now lost only one of their last seven league games and sit 10th in the table on 23 points.
"Gutted that we didn't win it. We fully deserved to win it," Arsenal manager Mikel Arteta said. "That's the quality of the opposition, so you cannot cry about it."
"We generated all the chances but it's so difficult to attack."
Arsenal had almost complete control of the ball in the first 10 minutes but Jimenez stunned the title-chasers in the 11th, racing away down the right and firing right-footed across goalkeeper David Raya into the far corner.
Declan Rice nearly scored a mirror-image goal for Arsenal at the other end midway through the half, controlling a pass from Leandro Trossard only to strike his left-footed volley just wide of Fulham keeper Bernd Leno's far post.
Despite having almost 75% possession in the half and four corners compared with none for the hosts, the Gunners were unable to break through Fulham's disciplined defence.
Saliba levelled for Arsenal shortly after the interval from point-blank range, poking the ball in when Kai Havertz headed it back down into his path from a corner.
Arsenal thought they had won it in the 88th minute when Bukayo Saka headed the ball in from close range, but the goal was ruled out by the video assistant referee for an offside in the buildup.
Fulham remained unbeaten in their last nine London derbies in the league, their best such run since 2000-2001.
"They're a good team and they know how to defend... but we didn't do enough today. We have to learn from that and make sure we strike back in the next one," Arsenal captain Martin Odegaard told Sky Sports.
In other games this morning Leicester City drew 2-2 with Brighton, while Bournemouth beat Ipswich town 2-1. West Ham face Wolves tomorrow morning.
