Manchester United closed in on the Premier League's pole position after a 2-1 home win over Aston Villa put them level on points and games played with champions and leaders Liverpool.
United trail their traditional rivals on goal difference, with both teams on 33 points from 16 matches ahead of their clash at Anfield on January 17.
Liverpool travel to Southampton on Tuesday (NZ time) while United visit Burnley on January 12.
United stretched their unbeaten league run to 10 games as Bruno Fernandes capped another fine individual performance with a penalty, after Bertrand Traore had cancelled out Anthony Martial's opener for the home side.
With striker Edinson Cavani serving a three-match ban for a social-media related offence, Paul Pogba got a start and put in a solid performance in the midfield as United ground out yet another tough win.
United right-back Aaron Wan-Bissaka, who constructed the home side's opening goal for Anthony Martial, was upbeat with the winners of a record 20 league titles looking to mount a credible challenge this term.
"The win means a lot, it shows where we've come from, from the start of the season," the 23-year old told the BBC.
"We're just taking it game by game. It was a late start for us, we were in catch-up mode, but we're here now. No excuses."
The hosts had the upper hand in the first half and Martial forced an acrobatic save from Emiliano Martinez, before he buried a superb diving header past the Villa goalkeeper after Wan Bissaka's fine cross in the 40th minute.
The visitors came close through Ollie Watkins, before Traore got on the end of a sharp Jack Grealish pass at the far post and beat United keeper David De Gea with a slick shot from close range in the 58th.
But Villa's joy was short-lived as Fernandes drilled his penalty into the bottom right corner three minutes later, after Paul Pogba went down under a challenge from Douglas Luiz, with the spot-kick given after a VAR check.
United pressed on and came close through Pogba as well as Fernandes and Marcus Rashford, before being forced to defend desperately in the dying minutes, with centre back Eric Bailly putting in a crucial stoppage-time block.
Hammers deal blow to Everton's title hopes
A late strike from Tomas Soucek gave West Ham United a 1-0 win at Everton in the first Premier League game of 2021 that had been short on fireworks, until the Czech midfielder's well-deserved winner in the 86th minute.
The Hammers lost goalkeeper Lukasz Fabianski to injury during the warm-up, but his replacement Darren Randolph barely had a save to make as Everton struggled to break down their rearguard.
It took until just before halftime for either side to register a shot on target as Everton's Brazilian winger Bernard fired a fizzing drive goalwards, but Randolph was alert to the danger and got down smartly to keep the ball out.
The introduction of Mikhail Antonio as a 59th-minute substitute provided a much-needed shot in the arm for West Ham and they had a flurry of chances in quick succession around the hour mark, but it was Soucek's late strike that sealed it.
His initial effort from the right forced a great save from Jordan Pickford who parried the ball away, but it was only cleared as far as Aaron Cresswell.
The West Ham fullback got plenty of power on his shot, which got a heavy deflection, before falling perfectly for Soucek to stab it home from close range.
Soucek's goal gave West Ham boss David Moyes his first victory at Goodison Park since leaving Everton in 2013.
"To come to Goodison Park and get three points and to play as well as we did ... we got the reward for it," a delighted Moyes told BT Sport.
"It was important to get something from this. It was our third game in six days, we asked the players to do it and they did a brilliant job."
The victory leaves West Ham 10th in the standings with 26 points while Everton, who could have gone second with a win, remain in fourth spot on 29 points, and boss Carlo Ancelotti was disappointed not to get more out of the game.
"The game was in the balance. We didn't have a lot of opportunities, they didn't have a lot of opportunities," he told BBC Sport.
"We have to accept the result. It will be important to keep our belief high ... We are in the position we would like to be and hopefully we can be there at the end of the season. That is our target."