Leaders Arsenal conceded and scored in the 90th minute to scrape past bottom-placed Wolves, while pursuing Manchester City and Aston Villa also picked up wins.
Elsewhere, Manchester United and Bournemouth played out a wild 4-4 draw at Old Trafford, Sunderland beat Newcastle 1-0 to earn Tyne-Wear derby bragging rights and Tottenham lost 3-0 at Nottingham Forest.
Using our player ratings system, Flashscore has selected its latest Premier League Team of the Week.
Goalkeeper
Gianluigi Donnarumma (Manchester City) - 7.9
Gianluigi Donnarumma made several key saves to backstop City's 3-0 win at Crystal Palace and keep his clean sheet intact.
He saved all four of Palace's shots on target and prevented 1.07 goals according to Expected Goals on Target (xGOT), which takes the placement of attempts into account.
Defenders
Malo Gusto (Chelsea) - 8.9
French defender Malo Gusto stole the show as Chelsea ran out 2-0 winners at home to Everton.
His pass set Cole Palmer through before he got on the scoresheet himself at the end of the first half to poke an effort into the net.
Gusto also made four clearances in the victory, where he recorded a Flashscore player rating of 8.9 for the highest of the week.
Calvin Bassey (Fulham) - 8.4
Fulham's towering Nigerian defender Calvin Bassey scored as the Cottagers eventually held off Burnley to win 3-2 on their travels.
Bassey buried a header which he couldn't miss and also won 10 duels and made four clearances in the Turf Moor encounter.
Pascal Struijk (Leeds) - 8.1
Pascal Struijk was on lockdown duty as Leeds claimed a 1-1 draw on the road at Brentford.
The Dutchman made a game-high 14 clearances to help the visitors come away from London with a deserved point.
Midfielders
Harry Wilson (Fulham) - 8.7
In an immense run of form, Harry Wilson contributed to all three of Fulham's goals in the win at Burnley.
A corner from the Welshman was nodded in to open the scoring, then his cross was directed in by Bassey for Fulham's second.
Wilson netted himself in the second half with a clinical finish into the bottom corner, which had an xGOT value of 0.87.
Bruno Fernandes (Manchester United) - 8.4
A stunning free-kick from Bruno Fernandes was one of many highlights in United's bonkers eight-goal draw with Bournemouth.
The Portuguese, who also grabbed an assist, wrapped his foot around the ball and planted it into the top corner to bring United level midway through the second half.
Ibrahim Sangare (Nottingham Forest) - 8.6
Two assists and a goal against Spurs ensured Ibrahim Sangare signed off on the best possible note as he heads off to the Africa Cup of Nations.
The Ivorian sealed a resounding Forest win with an effort from distance, while he also made two tackles and three clearances.
Morgan Rogers (Aston Villa) - 8.4
Morgan Rogers proved to be a livewire for Villa as his double lifted Unai Emery's side past West Ham 3-2.
Rogers' strike from the edge of the box proved to be the game-winner as Villa extended their winning run to nine games.
Callum Hudson-Odoi (Nottingham Forest) - 8.8
Two goals from Callum Hudson-Odoi ensured he ended an 18-game drought in style as Forest cruised to a comfortable victory.
His first was a simple tap-in, but the debate still goes on if his second was a cross or a shot as it sailed in over Guglielmo Vicario.
Forwards
Hugo Ekitike (Liverpool) - 8.7
Hugo Ekitike's two goals were all that was needed for Liverpool to see off Brighton 2-0 at Anfield.
The Frenchman netted in just 46 seconds and added his second on the hour mark with a fine header.
Erling Haaland (Manchester City) - 8.2
Premier League top scorer Erling Haaland was kept at bay at points by Palace but still came away with two goals in a big win.
An excellent header and a well-taken penalty made it 17 goals in 16 games for the league campaign as City continue to apply pressure at the top.