Liverpool strengthened their hold on a Champions League place with victory over West Ham, while bottom club West Brom lost again to increase their relegation concerns.
Liverpool beat the Hammers 4-1 at Anfield to move up to second, five points clear of fifth-placed Tottenham, who play on Sunday.
The Baggies lost 2-1 to Huddersfield, leaving them with just one win from 14 games under Alan Pardew.
Swansea are back in the relegation zone after they lost at Brighton.
The Swans were unbeaten in their previous five games under Carlos Carvalhal but went down 4-1 at the Amex Stadium. They are 18th on goal difference, while West Brom are seven points adrift of safety.
Watford, though, are six points away from the bottom three after Troy Deeney’s goal gave them a home win over Everton.
- Match report: Liverpool 4-1 West Ham
- Match report: Brighton 4-1 Swansea
- Match report: West Brom 1-2 Huddersfield
- Match report: Watford 1-0 Everton
Meanwhile, an own goal by keeper Jack Butland denied struggling Stoke victory at Leicester as the two sides drew 1-1. The point means Stoke remain in the relegation zone in 19th place.
Southampton moved out of the bottom three following a 1-1 draw at Burnley, who are winless so far in 2018.
Finally, Bournemouth came back from two goals down to draw 2-2 at home to Newcastle.
- Match report: Leicester 1-1 Stoke
- Match report: Bournemouth 2-2 Newcastle
- Match report: Burnley 1-1 Southampton
In the Scottish Premiership, Rangers moved to within six points of leaders Celtic by beating Hearts 2-0, while bottom club Ross County went down 2-0 at St Johnstone.
Championship leaders Wolves suffered their sixth defeat of the season as they went down 2-0 at promotion-chasing Fulham, who have now won eight home games on the bounce.
Sunderland remain at the foot of the Championship but scored a last-minute equaliser to draw 3-3 with north-east of England rivals Middlesbrough, while Aston Villa netted two late goals to beat Sheffield Wednesday 4-2 and move to within a point of second place.
- Match report: Rangers 2-0 Hearts
- Match report: St Johnstone 2-0 Ross County
- Match report: Sunderland 3-3 Middlesbrough
- Match report: Sheff Wed 2-4 Aston Villa