Manchester City and Arsenal closed in on Premier League leaders Liverpool with contrasting victories on Saturday as Manchester United's bubble was burst by Fulham.
IMAGES from the Premier League matches played in England on Sunday.
The battle for Champions League qualification continues with fourth-placed Aston Villa away to Luton Town on Saturday and Tottenham Hotspur, who are five points behind with a game in hand, hosting Crystal Palace.
Bernardo Silva and Jack Grealish scored three minutes apart as Manchester City came from behind to beat Premier League newcomers Luton Town.
Liverpool, beaten by Arsenal on Sunday, lead the table on 51 points from 23 games but City are up to 49 from 22 and Arsenal on 49 from 23.
Chelsea came from behind to beat Crystal Palace 3-1 thanks to added time goals from Conor Gallagher and Enzo Fernandez.
Arsenal closed the gap on leaders Liverpool with a 2-1 Premier League victory at Nottingham Forest
Liverpool reclaimed top spot in the Premier League with a 3-1 win over Burnley at Anfield on Saturday, but they were made to battle hard by a brave visiting side.
Vitaliy Mykolenko's 39th-minute own goal had put Luton ahead before Jack Harrison cheered the Everton faithful with an equaliser in the 55th minute, hammering in a low shot that Luton keeper Tim Krul allowed to let slip through his hands.
Arsenal's victory ended a run of three successive defeats in all competitions and put them level on 43 points with Aston Villa and champions Manchester City. Arsenal's goal difference is superior to Villa's but worse than City's.
Championship (second tier) side Rotherham, who haven't made it through to the fourth round of the competition since 2001-02, kept their composure early on as Fulham controlled the play.
Liverpool kicked off the new year three points clear atop the English Premier League standings with a 4-2 victory over Newcastle United.
IMAGES from the Premier League matches played on Saturday.
Liverpool moved back to the top of the Premier League with a 2-0 victory at struggling Burnley
'Not in the dressing room. Of course there are a lot of rumours but it is not that we get distracted by it.'
Aston Villa claimed their first three points of the Premier League Season
Just as the umpire's decision is no longer final, what is disdainfully rejected is the age-old dictum that the game should be played and watched in the spirit of the game, sighs Uddalok Bhattacharya.
Jarrod Bowen and Mohammed Kudus' second-half goals gave West Ham a 2-0 win over Manchester United in the Premier League's early game on Saturday, as the Hammers briefly moved into the top six.
Manchester United's Alejandro Garnacho scored with a magical overhead kick in the third minute to send the visitors on their way to a 3-0 victory over an Everton team already reeling in their first Premier League game after being docked 10 points.
Michael Olise scored a stoppage-time penalty as Crystal Palace clawed back from two goals down to draw 2-2 with Manchester City in the Premier League at the Etihad Stadium on Saturday.
IMAGES from Saturday's action in the English Premier League.
Manchester City roared back to the top of the Premier League with a 6-1 thrashing of Bournemouth after Manchester United steadied the ship
Manchester United were humbled 3-0 at home by Newcastle United in the League Cup fourth round
IMAGES from the Premier League matches played on Saturday.
A summary of Saturday's action in the English Premier League.
Wolverhampton Wanderers stunned Tottenham Hotspur 2-1 with stoppage-time goals from Pablo Sarabia and Mario Lemina on Saturday, thwarting the visitors in their bid to reclaim top spot in the Premier League table.
A summary of Sunday's action in the Premier League.
Kyle Walker extends Manchester City stay until 2026
Arsenal claimed their first Premier League win at Everton for six years as Leandro Trossard's second-half strike proved enough to secure the points at Goodison Park on Sunday.
Images from the English Premier League matches played on Saturday.
Images from the Premier League matches played on Saturday.
IMAGES from the Premier League matches played on Saturday
Champions Manchester City slipped to a shock first Premier League defeat of the season at Wolverhampton Wanderers on Saturday, while Manchester United's campaign of woe continued with a loss to Crystal Palace.
Images from the English Premier League matches played on Saturday
IMAGES from the English Premier League matches played on Saturday.
IMAGES from EPL matches played on Thursday.
Cody Gakpo scored his first goal for the club as they halted a dismal run
Diogo Jota and Mohamed Salah were on target as Liverpool edged Premier League strugglers Nottingham Forest 3-2.
IMAGES from the English Premier League matches played on Saturday.
England forward Marcus Rashford was on target again as Manchester United earned a nervy 3-1 victory over Everton in the FA Cup third round on Friday.