Timo Werner scored the only goal as Chelsea beat West Ham United to create a three-point gap over their opponents in the race for fourth.
Chelsea created the better of the first-half chances, Werner skewing over after only four minutes and Mason Mount forcing Lukasz Fabianski into a save.
Their persistence paid off two minutes before the break, when Ben Chilwell squared for Werner to score his first league goal since 15 February.
Werner missed a fantastic chance to double the lead 10 minutes after half-time, shooting wide from close range after Fabianski had parried Mount's effort.
West Ham pushed for an equaliser, their best chance falling to Jesse Lingard, whose shot dropped narrowly wide.
Their hopes of a point were hit by Fabian Balbuena's red card for a high challenge on Chilwell, awarded after a VAR review.
Chelsea stay fourth with 58 points, a place above West Ham with five matches to play.
West Ham: 3 May v Burnley (A)
Chelsea: 1 May v Fulham (H)
Referee: Chris Kavanagh. Assistants: Adam Nunn, Sian Massey-Ellis. Fourth official: Mike Dean. VAR: Peter Bankes. Assistant VAR: Andy Halliday.