Manuel Lanzini scored twice as West Ham claimed a 3-1 win in what could be an ignominious end to Sam Allardyce's reign as Everton boss.
Goals from Lanzini either side of a Marko Arnautovic effort which Jordan Pickford should have done better with earned the Hammers victory in what could also be David Moyes' last game as boss.
Allardyce, the former England and West Ham manager, was booed by visiting fans prior to Oumar Niasse making it 2-1 at the London Stadium, but there was to be no comeback.
Moyes' stock has risen in guiding West Ham to safety and, like with Allardyce, there are rumours over his future.
The Scot selected the same side as the one which began Thursday's goalless draw with Manchester United, another of his former clubs, and was rewarded with a first win over Everton at the sixth attempt.
Wayne Rooney, who played under Moyes at Everton and United, is the Toffees' leading scorer with 11, but was absent for Everton with a knee injury ahead of a rumoured move to Major League Soccer's DC United.
Allardyce pointed to the lack of a prolific goalscorer for Everton's travails, but the visitors could scarcely get a kick of the ball early on as Arnautovic had a shot blocked and Pickford denied Mark Noble.
Adrian was unhappy with Niasse for leaving his foot in as the goalkeeper cleared.
Adrian then saved with his feet from the striker after Angelo Ogbonna made a mess of an attempted clearing header.
Everton went behind when Lanzini started and finished a flowing move.
Lanzini combined with Pablo Zabaleta down the right and the full-back played the ball in field for Cheikhou Kouyate.
Kouyate's pass towards Arnautovic went by the Austrian untouched and was met by Lanzini, who showed composure to finish into the bottom corner.
There was another exchange between a goalkeeper and striker arriving late when Pickford stuck up his knee and directed it into Arnautovic's groin. Whether the mischievous act was seen by match officials was uncertain.
With Hammers fans booing, Everton attacked. Leighton Baines' cross was met by Niasse, but he could not direct his header on goal.
Niasse was making a nuisance of himself, but Arnautovic was more menacing and Phil Jagielka had to time a tackle well to deny the striker.
When Allardyce substituted Cenk Tosun for Theo Walcott after 61 minutes, the visiting Everton supporters made their feelings towards their boss known. Hammers fans laughed, having previously directed their own ire at Allardyce.
There was further reason for Everton discontent when Arnautovic turned Michael Keane with ease and struck a swerving ball which appeared to go through Pickford's despairing dive.
It was Arnautovic's 11th goal of the season and he had a 12th ruled out for offside.
A ferocious Niasse shot was pushed on to the post by Adrian, who was beaten by the same player soon afterwards.
West Ham failed to clear a corner and Niasse brought the ball down, turned and poked in.
The revival was short lived as Lanzini curled in from the edge of the area.
And there was to be no late rally from the visitors as Adrian saved in quick succession from Walcott and then Niasse.