Swansea City leapfrogged Hull City to climb out of the Premier League relegation zone with two games remaining after Fernando Llorente headed the winner against Everton.
Llorente got the better of Phil Jagielka to nod Jordan Ayew's cross past goalkeeper Maarten Stekelenburg from close range - the Spaniard's 13th league goal of the season.
Mason Holgate's last-ditch challenge prevented Alfie Mawson from making it 2-0 before Ayew hit the post from 16 yards.
Hull, who earlier lost 2-0 at home to relegated Sunderland, drop into the bottom three, while this result also means Middlesbrough will be relegated to the Championship if they lose to leaders Chelsea at Stamford Bridge on Monday (20:00 BST).