West Ham thumped Southampton 3-0 to move away from the relegation zone, Manchester City stayed on track to win the Premier League title next weekend and Manchester United and Liverpool both won to consolidate their top-four places.
Two goals from Marko Arnautovic and a Joao Mario strike put the Hammers up to 14th, five points above the bottom three, and left Saints in 18th.
There was heightened security at London Stadium but no repeat of the multiple pitch invasions and crowd disruptions seen in the loss to Burnley earlier this month.
- Match report: West Ham 3-0 Southampton
- Match report: Crystal Palace 1-2 Liverpool
- Match report: Man Utd 2-0 Swansea
- Match report: Everton 1-3 Man City
City restored their 16-point lead at the top with victory over Everton and will win the title if they beat rivals United next weekend.
Liverpool temporarily went second with a 2-1 win at Crystal Palace, thanks to Mohamed Salah's late strike.
But Manchester United went back above the Reds as Romelu Lukaku's 100th Premier League goal led the way for a 2-0 victory over Swansea.
- Sweeping up glass & cooking pasta - Kevin Davies mucking in at Southport
- Will Ferrell v Zlatan Ibrahimovic? Los Angeles FC prepare to face Galaxy on derby day
- From war-torn Afghanistan to Notts County - five inspiring stories from the week
Bottom side West Brom set a Premier League club record of eight successive defeats, going down 2-1 to Burnley - the Clarets' Ashley Barnes opened the scoring with a stunning bicycle kick.
Huddersfield continue to drift towards the relegation zone as their hosts Newcastle moved up to 12th, the only goal of the game coming from Ayoze Perez.
Glenn Murray's missed penalty proved costly for Brighton, as they went on to lose 2-0 to Leicester.
And Jermain Defoe rescued a late point for Bournemouth in a 2-2 draw at Watford.
- Match report: West Brom 1-2 Burnley
- Match report: Newcastle 1-0 Huddersfield
- Match report: Brighton 0-2 Leicester
- Match report: Watford 2-2 Bournemouth
In the Scottish Premiership, Celtic moved to within 10 points of guaranteeing a seventh successive Premiership title with a comfortable 3-0 victory over bottom side Ross County.
And in the Championship, Birmingham City climbed out of the relegation zone with a 1-0 win over Ipswich.