Romelu Lukaku and Aaron Lennon scored either side of what was to prove a costly red card for Kevin Mirallas to put the Toffees on course for a valiant victory. However, Michail Antonio and Diafra Sakho drew West Ham level, before Dimitri Payet's 90th-minute winner.
The defeat will certainly lead to a number of questions being asked and here are five talking points from the game - including why Mirallas is his own worst enemy.
An all too familiar story for the Toffees
Payet's 90th-minute winner completed a stunning late West Ham comeback, but it was another disappointing ending to an all too familiar story for Everton. For three-quarters of the match, Roberto Martinez's side were brilliant, but for the last 12 minutes it could not have got much worse.
This should have been an analysis of a valiant victory that gave the Toffees hopes of Europa League qualification a boost. Instead, this is the launch of another inquest into how Everton conspired to let yet another lead slip. However, this is not the first or second time this season that Everton have been undone after taking a two-goal lead.
Defensive errors, poor game management and a lack of ruthlessness are the same problems that have cost Everton so many points this season. Had Romelu Lukaku converted his penalty kick with just over 20 minutes to go, the Toffees would have been leading 3-0 and heading for a huge win in their pursuit of the top six. However, a lack of ruthlessness by Lukaku from the penalty spot was the trigger for West Ham's dramatic comeback.
There was more to it than just Lukaku's missed opportunities. The Toffees had to play more than an hour with just 10-men following Mirallas' dismissal, they produced a valiant effort with a man less, but ended up losing their heads and then ultimately running out of legs as the conclusion drew near.
When Michail Antonio pulled one back for the Hammers, a match that Everton were well on course to pass with flying colours, suddenly became that bit harder and those painful memories of Bournemouth, Stoke City and Chelsea came flooding back. Goals from Sakho and Payet then took matters to a whole new level of despair for Everton supporters and questioned their side's game management once again.
Mirallas is his own worst enemy
Kevin Mirallas certainly did not help himself or his team. If he hasn't already, Mirallas is close to using up every last bit of remaining patience Everton supporters have for the forward.
It is debatable whether the Belgian deserved a booking for his first offence after referee Anthony Taylor adjudged him to have dived. However, after that he only has himself to blame. To commit such a rash challenge was stupid, and on the halfway line with no danger even more so. His late challenge on Aaron Creswell was a definite booking and, not only proved costly for the Toffees, but it could prove costly for Mirallas on a personal level.
Some Everton supporters have been calling for Martinez to give Mirallas more game time, and just when he appeared to have won the trust back of the Everton boss after a sending off at Swansea City in September, he repeats the feat. And with Aaron Lennon impressing again and Gerard Deulofeu clicking his heels on the bench, will Mirallas get another look in this season with his place in doubt for Belgium’s Euro 2016 squad?
Defensive fragilities resurface
No side has conceded as many goals at home in the Premier League this season, but the Toffees have improved defensively over recent weeks keeping four clean sheets in their last six games in all competitions.
Roberto Martinez opted for three in defence, but supporters cannot blame the tactical tweaks for the defeat. The Toffees looked comfortable and in control with Phil Jagielka, John Stones and Ramiro Funes Mori across the back. It was only after Mirallas' exit and reverting to a back four that familiar fragilities returned.
Slaven Bilic brought both Andy Carroll and Diafra Sakho on as the Hammers opted for a more route-one approach and once again the Toffees were unable to withstand aerial bombardment. Three crosses, three goals, three points gone.
West Ham must hate the sight of Lukaku
It may have turned out to be a familiar story for Everton, but West Ham must have thought that it was going to turn out to be a familiar story and one that has given the Hammers nightmares over recent years.
Prior to Saturday, Romelu Lukaku had scored in all seven of his appearances against West Ham in an Everton shirt and he extended that run to eight successive games in the 13th minute. The Belgian turned Reece Oxford on the edge of the box to fire home off the post for his 18th Premier League goal of the season, his best ever tally, but you suspect there will be a lot more before the end of the campaign.
Lukaku did have opportunities to increase his season tally from the penalty spot, but he scuffed his shot and watched in disbelief as the ball tamely rolled towards Adrian. He had another chance not long after, but the West Ham goalkeeper was once more equal to his effort. There is no doubt, though, that the Belgian enjoys playing against the Hammers.
Aaron Lennon must be considered by England again
Aaron Lennon has not played for England since February 2013 when he came on as a substitute in a friendly against Brazil, but when he joined Everton permanently last summer he set his sights on an England recall.
The 28-year-old moved to Goodison Park to get the first team football needed to get back on the international stage and, although the winger has had to wait patiently for a run of games, he is now producing the form that warrants selection.
He got on the scoresheet for the sixth time in his last ten games and the pace and skill he showed in combining so well with Lukaku and finishing with calmness wasreminiscent of the confidence he is playing with. His rejuvenation at Goodison will surely put him in the conversation, at least, for a place in Roy Hodgson's next England squad.