Liverpool's Sadio Mane celebrates after scoring the winning goal during their Premier League match against Wolverhampton Wanderers at Anfield Stadium in Liverpool on Sunday. Photo: Jon Super/AP

LONDON – Liverpool restored their 13-point lead at the top of the Premier League on Sunday thanks to a hard-fought 1-0 win over Wolves at Anfield.

Sadio Mane scored the only goal of the game in the first half while VAR played its part as Jurgen Klopp's side extended their unbeaten run to 36 matches and moved further clear of Leicester.

Chelsea won 2-1 at Arsenal to close the gap on third-placed Manchester City, who were playing Sheffield United in the day's late game.

Wolves pushed Liverpool hard throughout at Anfield but Mane's 42nd-minute goal won it for the home side as they made it 55 points out of 57 at the halfway stage in the season.

Mane's goal was initially ruled out for a handball by Adam Lallana but VAR overturned the decision as the ball had come off his chest before Mane swept the ball home.

Wolves thought they had equalized through Pedro Neto but the goal was eventually ruled out by VAR for a marginal offside in the build-up.

Wolves had chances to level late on as Liverpool showed signs of tiredness but the home side hung on for their 10th win out of 10 at Anfield this season.

Earlier, Chelsea scored twice in five minutes as they won 2-1 at Arsenal to cement fourth place.

Pierre-Emerick Aubameyang put Arsenal in front early on but Jorginho equalized on 83 minutes and Tammy Abraham won it four minutes later.

Arsenal dominated the first half but paid the price for a goalkeeping mistake by Bernd Leno which allowed Jorginho to tap home.

Abraham swept in the winner after nice play with Willian but it was the introduction of Jorginho off the bench in the first half that changed the game.

"We were so awful for 30 mins, slow lethargic, nervous," Chelsea manager Frank Lampard said. 

"The opposite of against Tottenham. We gave Arsenal everything they wanted. We made the change early, felt it had to be done. Second half we dominated.

"After 10 mins or so it was clear that Arsenal had seen us play against Tottenham and made us into a back five instead of a back three. They were on top and there was a lack of balance to our team. The sub gave us another man in midfield and gave us more urgency."

Lampard said Chelsea still needed to sort out their home record, a problem emphasized by their loss to Southampton on Boxing Day.

"Our next home games we'll do everything we can to turn the corner," he said. 

"We're still in fourth and want more and the home games have been different so we have to focus on them when they come around."

Arsenal defender David Luiz said the side showed signs that they will soon be back up the table under new manager Mikel Arteta.

"It is not easy for him in the middle of the season, he didn't choose the players, but he will do his best," Luiz said. 

"That's why we could see Arsenal dominate in the first half with amazing football and quality. We should (have) scored a second goal and then it would be a different game.

"But congratulations to Chelsea. Frank has come in and they're doing what he wants them to do."