Laurent Koscielny scored for Arsenal, as the Gunners cemented their position at the top of the Premier League table with a 1-0 win over Newcastle United at the Emirates.
Manchester United also returned to winning ways after beating Swansea City 2-1 at Old Trafford. Wayne Rooney finally broke his goal scoring drought as United ended their 8-games winless streak.
In the early kick off, Andy Carroll scored against his former club Liverpool, as the Hammers produced an emphatic performance, winning 2-0 at Upton Park.
Artur Boruc saved a crucial penalty from Riyad Mahrez, as Bournemouth maintained their undefeated run to eight games after earning a 0-0 draw against Leicester.
Manchester City face a tough game away to Watford, while derby rivals Manchester United face Swansea City at home.
Chelsea registered their first Premier League victory under Guus Hiddink, after they won 3-0 against Crystal Palace at Selhurst Park.
Premier League Week 20 Results
West Ham 2-0 Liverpool
Arsenal 1-0 Newcastle
Leicester 0-0 Bournemouth
Man Utd 2-1 Swansea
Norwich 1-0 Southampton
Sunderland 3-1 Aston Villa
West Brom 2-1 Stoke City
Watford 1-2 Man City
Crystal Palace 0-3 Chelsea
Everton 1-1 Tottenham
EPL Table from Week 20