Results and images from the English Premier League matches played on Saturday
Chelsea were given a stiff examination by Stoke City at Stamford Bridge on Saturday before extending their lead at the top of the Premier League to nine points ahead of the late game between Liverpool and Manchester City.
Willian scored twice as a spirited Stoke were beaten 4-2 despite twice coming back to equalise.
That made 13 successive victories for Antonio Conte's side, equalling the record by any club for a single season in the top division of English football.
They were pushed hard, however.
After defender Gary Cahill headed in a corner, Dutch international Bruno Martins Indi brought Stoke level. Willian then scored twice in eight minutes in the second half, on either side of Peter Crouch tapping in for his first Stoke goal since May 2015.
Chelsea could not feel secure until Diego Costa, back after suspension, scored his 14th of the season.
Sixth-placed Manchester United fell behind at home to Middlesbrough before goals from Anthony Martial and Paul Pogba in the last five minutes brought about a 2-1 win.
Aitor Karanka had proved a match for his mentor Jose Mourinho, under whom he once worked at Real Madrid, and Grant Leadbitter scored for the visitors midway through the second half after Alvaro Negredo nodded down a cross for him.
It was Middlesbrough's first attempt on target.
Zlatan Ibrahimovic, with 11 goals in his previous 10 games, was annoyed to have a 12th ruled out in the first half, for a high foot.
Martial, who had earlier hit a post for United, brought them level with only five minutes to play and a minute later Pogba earned United their fifth successive league win.
Leicester ease relegation fears with 1-0 win over Hammers
Striker Islam Slimani scored the only goal as champions Leicester City beat West Ham United 1-0 on Saturday to climb six points clear of the Premier League relegation zone.
Slimani, who had earlier hit the post, met Marc Albrighton's cross with an emphatic header past keeper Darren Randolph after 20 minutes.
Leicester's fifth victory in 19 league matches lifted them to 15th with 20 points and ended a run of three wins for West Ham, who came closest when Michail Antonio's shot hit the bar.
The victory rewarded Leicester for their fine opening half hour after which West Ham took control and dominated possession but failed to score despite twice as many shots as their opponents.
Bournemouth add to managerless Swansea's misery with 3-0 win
Bournemouth thrashed Swansea 3-0 with first-half strikes from Benik Afobe and Ryan Fraser followed by a late one from Joshua King, leaving the Swans nailed to the bottom of the Premier League table.
Eddie Howe's Cherries took the lead in the 25th minute with Afobe scoring from close range on the rebound after Jordi Amat narrowly avoided deflecting the ball into his own net.
Fraser raced into the area in stoppage-time at the end of the half to smash in a Junior Stanislas cross, doubling the visitors' lead.
Swansea, under caretaker manager Alan Curtis, struggled to gain possession throughout the second half, before Bournemouth substitute Joshua King shot past goalkeeper Lukasz Fabianski to seal the win.
Gray grabs hat-trick as Burnley thrash Sunderland
Andre Gray celebrated his maiden Premier League hat-trick as Burnley headed into the New Year sitting comfortably in mid-table after a 4-1 demolition of struggling Sunderland at Turf Moor.
The 25-year old striker opened the scoring in the 31st minute, powering the ball past goalkeeper Vito Mannone after two Sunderland defenders collided.
He added a brace in the space of two minutes early in the second half before Ashley Barnes completed the rout with a 67th-minute penalty.
Jermain Defoe pulled one back for Sunderland after a fine solo run by Adnan Januzaj, but it was scant consolation for the Black Cats, who remain in the relegation zone in 18th place with 14 points from 19 games.
Late Barkley goal earns Everton a point at Hull
England midfielder Ross Barkley headed a late leveller to salvage a 2-2 draw for Everton at Hull City in the Premier League on Friday.
Barkley headed the ball home in the 84th minute from left back Leighton Baines' cross after Robert Snodgrass had put Hull ahead with a superb free kick into the top corner 19 minutes earlier.
Defender Michael Dawson had given Hull an early lead when he scored from Curtis Davies' flicked pass in the sixth minute but an own goal by home keeper David Marshall at a corner gifted Everton an equaliser on the stroke of halftime.
Hull, who had lost five of their previous seven matches, climbed to second from bottom in the table with 13 points from 19 matches. Everton are seventh with 27 points, 19 shy of leaders Chelsea.
City manager Mike Phelan refused to criticise Marshall for his own goal.
"Mistakes happen," said Phelan. "In the second half he pulled off a couple of important saves.
"I think it's a terrific point. We produced a battling performance and I'm pleased with the players. We are in a battle for the rest of the season but we're up for it."
Everton manager Ronald Koeman praised his team's battling qualities.
"I'm really pleased with our performance," said the Dutchman. "I wasn't happy with our slow start but we showed a really good attitude and reaction twice.
"We played good football and created a lot of opportunities. We keep the momentum after the win against Leicester -- two away games and four points is good."