The Toffees extended their unbeaten run against West Ham to 12 matches, having won eight of those.
As for Romelu Lukaku's goal, it was set up by Leighton Baines, which was the full-back's first assist of the season.
Meanwhile, the Hammers have lost half of their 14 away matches this term.
Fulham 1-3 Chelsea
Andre Schurrle's trio of goals means that the last three Premier League hat-tricks have been scored by Chelsea players. The other two were Samuel Eto'o and Eden Hazard.
Talking of Hazard, statisticians Opta revealed that he was the first player this season to have completed 100 dribbles.
The three Chelsea goals took Fulham's conceded tally to 62 from their 28 matches.
Hull City 1-4 Newcastle United
Hull's recent negative run of form continued with this defeat, having won just one of their last seven outings.
The Tigers have also been defeated in 12 of the 13 matches in which they have conceded the first goal.
Two of visiting Newcastle's goals were scored by Moussa Sissoko, which were his first for the club in the Premier League away from St James' Park.
Stoke City 1-0 Arsenal
Jonathan Walters scored from the penalty spot for Stoke, having missed his previous three kicks from 12 yards.
The penalty was conceded by Arsenal centre-back Laurent Koscielny, who has now given away six since he joined the Gunners in 2010.
During the second half, Arsenal failed to record a single shot on target.
Southampton 0-3 Liverpool
Luis Suarez ended a run of five matches without a goal when he scored the opener at the St Mary's Stadium.
That took his goals tally for the campaign to 24, while he has also made 10 assists for his Liverpool teammates.
Meanwhile, the hosting Saints have failed to win nine of their 14 home encounters.
Aston Villa 4-1 Norwich City
No player can match Christian Benteke's return of five headed goals so far this season.
The Belgian's brace also helped Villa to score four goals in the first-half of a Premier League game for only the second time.
Beaten Norwich have now won just four of their 33 away fixtures under the management of Chris Hughton.
Swansea City 1-1 Crystal Palace
A knee injury suffered in May has limited Glenn Murray's appearances this season, but the striker scored his first goal since making his return to action at the Liberty Stadium.
The penalty that he scored was the 21st that the Eagles have been awarded since the start of last season.
As for Swansea, they are unbeaten from their last meetings with Palace.
Tottenham Hotspur 1-0 Cardiff City
Having waited since October 20, Roberto Soldado scored for Spurs from open play.
The Spanish centre-forward has now fired in six Premier League goals for the North Londoners since his summer switch from Valencia.
Staying with the goals theme, Cardiff have now failed to score in six of their previous seven matches against Tottenham.
