Chelsea fought off a dogged Stoke for a record-equaling 13th successive Premier League win as Liverpool maintained its pursuit of the leaders with a victory over Manchester City.
Thanks to Saturday's 4-2 win, Chelsea will enter the second half of the season holding a six-point advantage over Liverpool in Antonio Conte's first season in charge of the London club.
Juergen Klopp is also satisfied with Liverpool's progress as he looks to deliver the club's first title since 1990 by chasing down Chelsea over the next 19 games.
"Can you imagine how annoying it is when you have won 13 games in a row and another team is only six points behind," Klopp said after Liverpool's 1-0 win over City. "It is unbelievably difficult this league."
It was Pep Guardiola with little to celebrate on New Year's Eve as City slipped 10 points behind leader Chelsea.
CHELSEA 4, STOKE 2
Chelsea has emulated Arsenal's 2002 side by reeling off 13 wins in a row in the same season and it's thanks to Willian's double.
Goals from Gary Cahill and Willian were canceled out by Stoke duo Bruno Martins Indi and Peter Crouch. When Willian put Chelsea in front for a third time in the 65th minute, Stoke could find no way back this time and Diego Costa added a fourth.
"When you win a lot there is a great danger to be satisfied, to be relaxed, to think, 'OK, but we won a lot in the past, now if arrive the draw, if we don't lose, if we don't win it's not important,'" Conte said. "No. My players showed me great will, great will to fight, great will to win, great will to take this great achievement for us. I'm pleased for them and they deserved this. I'm their coach, but they deserved this."
LIVERPOOL 1, MAN CITY 0
Georginio Wijnaldum's eighth-minute header secured Liverpool's fourth successive league win. Wijnaldum will take the plaudits for providing his second goal of the season, but Adam Lallana's contribution underscored how the midfielder is an essential ingredient in the title bid.
It was Lallana's seventh assist of the season — he has also scored seven — that set up Wijnaldum. The Dutch midfielder climbed above City defender Aleksandar Kolarov to meet Lallana's well-placed cross from the left flank before planting a header beyond goalkeeper Claudio Bravo.
"It was kind of a wild game," Klopp said. "It was intense. It's not about having a philosophy, it's about adapting to the quality of the opponent and in this case we needed to defend from a compact formation."
MAN UNITED 2, MIDDDLESBROUGH 1
Anthony Martial and Paul Pogba scored late goals in the 85th and 86th minutes to rescue a fifth successive win for Jose Mourinho's United.
Grant Leadbitter had given Middlesbrough the lead but United gave the watching former manager Alex Ferguson the perfect 75th birthday gift.
"If the fans remember this not just for Sir Alex's birthday but for the kind of performance we had, I think it's a great tribute," Mourinho said.
United's in-house television channel received a shock after the game when nine-time Olympic Usain Bolt called in with his analysis.
LEICESTER 1, WEST HAM 0
Leicester moved six points clear of the relegation zone on Saturday after the struggling champions ended a three-game winless streak courtesy of Islam Slimani's header. Leicester moved up one spot to 15th.
SWANSEA 0, BOURNEMOUTH 3
Swansea's miserable form continued in the first game following Bob Bradley's firing. Benik Afobe and Ryan Fraser scored first-half goals and substitute Josh King completed a comfortable win for Bournemouth in the 88th minute.
SOUTHAMPTON 1, WEST BROM 2
In the final five minutes of the first half, Shane Long put Southampton ahead and Matt Phillips equalized. But Hal Robson-Kanu struck a second-half winner for West Bromwich Albion before Southampton defender Virgil van Dijk was sent off in the 88th for bringing down striker Salomon Rondon.
BURNLEY 4, SUNDERLAND 1
Burnley moved closer to mid-table safety powered by Andre Gray's hat trick against relegation-threatened Sunderland.
Fourth-placed Arsenal and fifth-placed Tottenham are both in action on New Year's Day. Tottenham is at Watford before Arsenal hosts Crystal Palace.