Premier League results: Southampton, Swansea, Stoke, Burnley, Everton, Crystal Palace
Southampton moved to within a point of Premier League safety after beating Bournemouth, while West Brom won at Newcastle to keep alive their own slim survival hopes.
Matt Phillips scored the Baggies' winner at St James' Park, where Ben Foster produced a fabulous save in a 1-0 victory.
Saints sealed their first league win under manager Mark Hughes with a Dusan Tadic double, hours after fellow strugglers Stoke held Liverpool to a 0-0 draw at Anfield.
Swansea's 1-0 home loss to Chelsea ensured that the Baggies' Premier League place is secure for another week at least.
Elsewhere, Crystal Palace moved further clear of the relegation zone and into 11th with an impressive 5-0 victory at home to Leicester, while Everton beat Huddersfield 2-0.
That result means the Terriers are just three points clear of the bottom three with three games to play, while Burnley will have to wait for confirmation of seventh place and a spot in the Europa League next season.
Sean Dyche's side remain six points clear of eighth-placed Everton with two matches to play and a goal difference superior by 15 goals after they drew 0-0 at home to Brighton.
On Sunday, West Ham host champions Manchester City (14:15), while Manchester United welcome Arsenal (16:30).
Tottenham play at home to Watford on Monday (20:00).
- Match report: Liverpool 0-0 Stoke
- Match report: Burnley 0-0 Brighton
- Match report: Crystal Palace 5-0 Leicester
- Match report: Huddersfield 0-2 Everton
- Match report: Newcastle 0-1 West Brom
- Match report: Southampton 2-1 Bournemouth
- Match report: Swansea 0-1 Chelsea
In the Scottish Premiership, fourth-placed Hibernian beat fifth-placed Kilmarnock 5-3.
In the Championship, Cardiff beat Hull to move back into the automatic promotion spot of second place.
MK Dons were relegated from League One after they lost 2-0 to Scunthorpe.
Accrington Stanley won the League Two title after a 1-0 victory over Lincoln City, and Wycombe were promoted to League One after a 2-1 win at Chesterfield.