West Ham face a tough task to finish in the Premier League top four after Dominic Calvert-Lewin saw Everton run out winners at the London Stadium.
Calvert-Lewin's 24th-minute goal proved decisive against a Hammers side who huffed and puffed but never really hit their stride on a crucial afternoon, failing to register a single shot on target.
The closest West Ham came to an equaliser was when Vladimir Coufal's shot hit the post and Jarrod Bowen could not bundle in the rebound from point-blank range.
Everton hit the post late on through Josh King and they hung on for the win that keeps them in the frame for a European spot.
West Ham remained in fifth place with 58 points, five points behind fourth-placed Leicester City with three games remaining. Liverpool are only a point behind West Ham with a game in hand.
Everton are eighth with 55 points and have four games left.
