Manchester United suffered a 2-1 loss to Norwich City at Old Trafford to increase the pressure on manager Louis van Gaal.
United have now won just four of their last 15 matches in all competitions, while the defeat was their second in a row following last Saturday's 2-1 slump at Bournemouth.
Norwich went in front seven minutes before half-time when Cameron Jerome raced clear before thumping the ball past goalkeeper David De Gea.
The Canaries doubled their lead on 55 minutes when Jerome fed Alexander Tettey, who poked the ball in from the edge of the area.
Anthony Martial pulled a goal back for United, the France international forcing his way through before scoring beyond goalkeeper Declan Rudd.
Chelsea returned to winning ways following the departure of Jose Mourinho as they beat Sunderland 3-1 at Stamford Bridge on Saturday.
Mourinho, who left the club on Thursday, has been replaced by Guus Hiddink, who was in attendance against Sunderland following his appointment before kickoff, as Steve Holland oversaw the side
The Blues took the lead in the fifth minute through Branislav Ivanovic, who headed home from a Willian corner.
Chelsea doubled their advantage on 13 minutes when Pedro reacted quickest to a loose ball before thumping past goalkeeper Costel Pantilimon.
It was 3-0 early in the first half after Willian was felled by Pantilimon, with Oscar scoring from the spot.
Sunderland pulled a goal back through Fabio Borini, who bundled the ball in following a parry by Thibaut Courtois.
Two penalties from Riyad Mahrez saw Leicester beat Everton 3-2 at Goodison Park and open up a five-point lead at the top of the table.
Mahrez kept up his impressive form by keeping his cool from penalty spot against goalkeeper Tim Howard, after Shinji Okazaki was brought down by Funes Mori.
Romelu Lukaku scored for a seventh Premier League match in succession on 32 minutes, lashing in to make it 1-1 from close range.
Leicester retook the lead through Mahrez again, who scored his second penalty of the match -- and his 13th league goal of the season -- after Howard brought down Jamie Vardy.
It was 3-1 in the 69th minute when Vardy picked out Okazaki, who made no mistake to extend Leicester's advantage.
Kevin Mirallas scored a late consolation for the Toffees, the Belgium international scoring from close range.
Tottenham Hotspur bounced back from their loss at home to Newcastle last weekend by seeing off Southampton 2-0 at St Mary's.
Harry Kane scored just before half-time to make it 1-0 to Spurs, the England striker beating two men before finishing clinically.
More poor Southampton defending allowed Tottenham to double their lead when Dele Alli tapped in from close range from Kyle Walker's cross.
Lee Chung-Yong's superb goal in the 89th minute clinched a 2-1 win for Crystal Palace at Stoke.
Connor Wickham made it 1-0 to Palace just before the half-time whistle, hammering in from the penalty spot after Glenn Whelan fouled Wilfried Zaha.
Stoke restored parity after a handball from Damien Delaney, allowing Bojan Krkic to dispatch his spot kick.
With a minute left on the clock, Lee thrashed in a stunning shot from around 30 yards out.
Bournemouth won their third game in a row as they beat nine-man West Brom 2-1 at The Hawthorns.
The home side were reduced to 10 men in the 34th minute after James McClean made a late challenge on Adam Smith.
Bournemouth made their numerical advantage pay early in the second half when Adam Smith shot low past goalkeeper Boaz Myhill.
Pulis' West Brom hit back with 11 minutes remaining with Gareth McAuley glancing a header in to make it 1-1.
Charlie Daniels scored the winning goal from the spot with three minutes left after Dan Gosling was brought down, while Salomon Rondon was sent off in added time.
In the evening game, Jordan Ayew's screamer salvaged a point for Aston Villa as they drew 1-1 draw against Newcastle United in difficult conditions at St James' Park.
Fabricio Coloccini opened the scoring for Newcastle on 38 minutes, continuing their good form after back-to-back wins.
However, after Siem de Jong missed a golden chance, Villa hit back through Ayew, who thundered home in the 61st minute on a rain-soaked pitch.