The Spain international converted the all-important winner as the Blues momentarily moved nine points clear at the top of the Premier League table
Chelsea equalled their longest Premier League winning run by beating Crystal Palace 1-0 on Saturday for their 11th consecutive victory.
The league leaders were already guaranteed to be top of the tree at Christmas and a first-half goal from Diego Costa extended a run that stretches back to October 1.
Chelsea last won 11 on the bounce during their 2009-10 title-winning season and have been crowned champions each time they have previously topped the table on Christmas Day.
Costa’s opener came at the end of a drab first half but marked a sparkling return to form for the Spain international, whose 13th Premier League goal of the season takes him beyond his tally for the entire 2015-16 campaign.
He got his head to an excellent Cesar Azpilicueta cross to get the better of Palace goalkeeper Wayne Hennessey two minutes from the break, proving enough to secure maximum points.
Chelsea’s joy at moving nine points clear of Liverpool and Arsenal at the summit was tempered somewhat by yellow cards for Costa and N’Golo Kante, who are now suspended for the Boxing Day clash with Bournemouth.
Cesc Fabregas’ winning goal at Sunderland in midweek was not enough for him to retain his place in the Chelsea starting XI, dropping to the bench in one of two changes made by Antonio Conte.
Willian – one of the men to come in – was central to the visitors’ first meaningful attack.
Following a tepid opening in the Selhurst Park fog, the Brazilian exchanged passes with Eden Hazard on the edge of the box before Joel Ward obstructed the Belgian to concede a free-kick 20 yards out.
David Luiz’s low effort deflected wide off a Palace defender and the home side were soon threatening at the other end – Jason Puncheon scuffed his strike from a Martin Kelly cross to send the ball wide of the target.
In a half of few clear-cut chances, Palace were having most joy down the right, with Kelly whipping in another cross that James McArthur headed just wide.
Another attack down that flank resulted in a free-kick when Wilfried Zaha – earlier involved in a minor squabble with Damien Delaney over the make-up of a wall – was brought down just outside the box, but Jason Puncheon curled just over from the set-piece.
It was Chelsea who eventually snatched the lead just before the break, Costa getting his head on the end of a superb hanging cross from Azpilicueta to send the ball looping over Hennessey – the game’s first effort on target and the striker’s 50th Chelsea goal.
Thibaut Courtois was forced into a save from Yohan Cabaye early in the second half, before Kante tested Hennessey with a strike from 25 yards.
Marcos Alonso then drove a volley into the side-netting as he picked up the pieces from an intercepted Victor Moses cross after 67 minutes, while Fabregas – on for Willian – guided a tame effort straight at Hennessey.
Chelsea continued to look the more likely to score the game’s second goal, with Hennessey getting down well to his right to keep out Kante before Alonso rattled the crossbar from a free-kick, but they had to settle for a one-goal margin to put real distance between themselves and their title rivals.