Mauricio Pochettino's side were in complete control when Palmer scored his second goal to put the visitors three up with 20 minutes to play.

Palmer had opened the scoring at Kenilworth Road before Noni Madueke doubled Chelsea's lead late in the first half.

But former Chelsea midfielder Ross Barkley netted to spark a spirited finish from third bottom Luton, who scored again through Elijah Adebayo in a dramatic finale.

Chelsea's second consecutive win was their first success away from home since a victory at Tottenham on November 6, ending a four-game losing streak on their travels.

If that was encouraging for Pochettino, the manner of their late bout of nerves suggested there is still much to work on for an inconsistent team languishing in 10th place.

"I'm so pleased because we need to be great to beat Luton. It's difficult to play here," Pochettino said.

"We are a young team. They need to work together to create this trust and confidence.

"This type of result when you need your team-mates to fight with you will be a really good thing."

On Chelsea defender Thiago Silva's visible frustration at the final whistle, Pochettino added: "Thiago is like this. He is always moaning and never happy but that is good."

Pochettino's first competitive win as Chelsea boss came in the reverse fixture against Luton back in August.

But they have struggled badly since then and arrived at Luton hoping to avoid finishing 2023 with a 20th league defeat in the calendar year.

A self-described "football romantic", Pochettino admitted this week that he was relishing the opportunity to play against a club who just a few years ago were fighting to avoid extinction in the lower leagues.

But Pochettino also warned his young team they would get a taste of "real football" on their trip to ramshackle Kenilworth Road.

Nestled amid tight rows of terraced houses, Luton's tiny stadium is the antithesis of the Premier League's glamour clubs.

Chelsea initially appeared quite at home in their gritty surroundings as they quickly seized the momentum.

Palmer's early strike was held by Luton keeper Thomas Kaminski, but it was a statement of intent that presaged Chelsea's opener.

- Predatory Palmer -

Luton were culpable as a poor clearance inside their own area went straight to Palmer, who accepted the gift with a clinical finish into the far corner for his seventh goal since signing from Manchester City in September.

Pochettino had rewarded Madueke with a start after he came on to score the winner against Crystal Palace and the young winger repaid his manager's faith in the 37th minute.

Picked out by Palmer on the edge of the area, Madueke was allowed too much time by Luton's defence as he unleashed a fierce strike that flashed into the roof of the net at the near post.

With Chelsea less dynamic in the second half, Christopher Nkunku was sent on for Armando Broja as the Chelsea forward steps up his return to action after a long injury absence.

Palmer appeared to have put the result beyond doubt in the 70th minute when he sprinted onto Jackson's pass, cleverly rolled the ball around Kaminski and slotted home from close-range.

But Chelsea wobbled with the finish line in sight -- Adebayo having a goal ruled out for offside hinted at a Luton revival.

Adebayo then hit the bar with a header before Barkley glanced his header into the far corner from a Luton corner in the 80th minute.

And seven minutes later, Adebayo poked home from virtually on the goalline after Chelsea keeper Djordje Petrovic could only parry Alfie Doughty's header into his path.

Luton laid siege to the Chelsea goal in the final minutes, but the visitors escaped with a barely deserved victory.