Manchester United suffered a third consecutive defeat with Norwich City winning 2-1 for their first victory at Old Trafford since 1989.
The result meant that United drop out of the top-four on the table headed by Leicester City.
Meanwhile, Chelsea began the post-Jose Mourinho era with a 3-1 victory over Sunderland at Stamford Bridge to ease away from the Premier League's bottom three while Leicester City moved five points clear at the top.
15 J Vardy (Leicester)
13 R Lukaku (Everton)
R Mahrez (Leicester)
10 O Ighalo (Watford)
9 O Giroud (Arsenal)
H Kane (Tottenham)
As the home fans sang the name of the man who was sacked on Thursday after Chelsea's worst start to a season since 1978 and newly appointed interim coach Guus Hiddink watched from the stands, goals from Branislav Ivanovic, Pedro and Oscar restored some sense of normality in west London.
Leicester's remarkable title challenge continued with a 3-2 victory at Everton that ensures they will spend Christmas top of the table, a year after occupying bottom place heading into the hectic holiday schedule.
Two Riyad Mahrez penalties and a goal from Shinji Okazaki put Leicester on 38 points from 17 games, with chasing Arsenal and Manchester City, who clash on Monday, on 33 and 32 respectively.
Tottenham Hotspur took advantage of United's woes to move into fourth place thanks to a 2-0 win at Southampton while Crystal Palace remain sixth after a 2-1 win at Stoke City.
Bournemouth claimed a third consecutive league victory with a late Charlie Daniels penalty sealing a 2-1 victory at West Bromwich Albion who had James McClean sent off in the first half and Salomon Rondon in stoppage time.
Chelsea 3-1 Sunderland
Everton 2-3 Leicester City
Manchester United 1-2 Norwich City
Southampton 0-2 Tottenham Hotspur
Stoke City 1-2 Crystal Palace
West Brom 1-2 Bournemouth