Chelsea survived a spirited late fightback by Luton to edge a dramatic match 3-2 at Kenilworth Road and end their four-game losing streak away from home.

Mauricio Pochettino’s side looked to be cruising to a first victory on the road since early November thanks to two goals from Cole Palmer – his second a sensational piece of individual skill – and one from Noni Madueke who scored for the second time in two games as the visitors took a 3-0 lead.

But that breathing room was sucked away by Luton during a frenetic final 10 minutes, when first Ross Barkley then Elijah Adebayo struck to offer their supporters hope of a spectacular recovery.

Yet Chelsea held their nerve, claiming back-to-back league wins for just the second time under Pochettino.

They had taken the lead after 12 minutes and it was a gift from Luton.

First, the defence was caught out up the pitch and allowed Nicolas Jackson to run in from the left and through on goal. His effort was saved well by the legs of Thomas Kaminski and the ball fell at the feet of Issa Kabore, who instead of clearing his lines played an inexplicable pass straight to the lurking Palmer who took a touch and lashed it home.

Luton looked to Barkley, the former Chelsea player, for a response and he nearly provided it almost instantly, hitting a free-kick from 20 yards out that curved around the wall and cleared the bar by inches.

Chelsea were on their worst run of away league defeats in 23 years, whilst Luton had just recorded back-to-back top-flight wins for the first time this season. Yet in the first half the visitors posed much the clearer threat, attacking with a directness that has often been lacking on the road.

After 37 minutes they got their second, and it was Madueke fresh from scoring the winner against Crystal Palace on Wednesday that got it.

The ball was worked from the left flank over to the right via Palmer playing in the number 10 role. He moved it on again to Madueke, whose route to goal was barred by Amari’i Bell. Luton’s captain backed off, encouraging the Chelsea winger to run outside him and find space to thump the ball high inside the near post into the top corner.

Luton’s key creative outlets, Barkley and Andros Townsend, had been largely nullified by Chelsea’s determined pressing and harrying.

Palmer slotted easily back into his role as the visitors’ principle attacking outlet after serving a one-match suspension, whilst Jackson and Armando Broja were lively and Malo Gusto looked an increasingly able deputy to the injured Reece James at right-back.

The third goal when it came on 70 minutes was well deserved.

Jackson was clever and strong in midfield to spin away from his man and play an early ball through the middle to Palmer. Kaminski raced out to meet him, but as Palmer reached it he outfoxed the Luton goalkeeper with the deftest roll of the ball beneath his studs, sat the covering Albert Sambi Lokonga down and knocked in Chelsea’s third.

Adebayo thought he had got one back when he headed in Alfie Doughty’s cross, but VAR called offside against the winger, before Adebayo headed his next chance against the bar.

There was life in Luton and they proved it with two goals in seven minutes to stun Chelsea.

First, Barkley headed what looked a consolation from a corner, then Adebayo reacted quickest to turn the ball home after Djordje Petrovic had saved from Doughty.

Luton pushed and pushed in the closing minutes but a determined Chelsea held firm.