Wayne Rooney scored a hat trick, which included a blast from the center circle.
A Wayne Rooney hat trick, including one from inside his own half, helped Everton dish out thrashing to former manager David Moyes' West Ham side to give interim manager David Unsworth the perfect send off as the newly appointed Sam Allardyce watched from the stands.
West Ham made just one change from the side that drew 1-1 with Leicester on Friday, as Andre Ayew replacing Andy Carroll up front, with the Englishman dropping out of the squad altogether after picking up an injury in training.
Having had almost two full days less to prepare for this fixture following Sunday's 4-1 thrashing at Southampton, David Unsworth made five changes for his final game in caretaker charge of Everton.
Of the back four only Jonjoe Kenny remained, with Ashley Williams, Cuco Martina, and Mason Holgate coming in for the injured trio of Michael Keane, Phil Jagielka and Leighton Baines, while Tom Davies replaced Morgan Schneiderlin in holding midfield and Wayne Rooney returned to the lineup at the expense of Kevin Mirallas.
After a cagey opening quarter of an hour, it was Everton who took the lead. With just about their first dangerous attack of the game, Gylfi Sigurdsson played Calvert-Lewin in one on one with Joe Hart, and the England 'keeper came flying out of his goal, bringing down the young forward as he dived for the ball.
Despite Hart's protestations that he got the ball, referee Michael Oliver felt the England 'keeper made enough contact with Calvert-Lewin to point to the spot, though the West Ham stopper escaped a booking.
Up stepped Rooney, and despite seeing his penalty saved well down to his left by Hart, the Everton captain reacted quickest to head the rebound past his former England teammate to give the home side a vital lead.
Though that goal failed to open the game, Everton doubled their lead 10 minutes later. Breaking into the West Ham half, Jonjoe Kenny played a well timed pass down the line for Tom Davies, and when the midfielder's pull back found the advancing Rooney in the center of the area, the forward gleefully slotted home his, and Everton's second of the game into the bottom corner.
Despite pressing forward in an attempt to get themselves back into the affair, West Ham were unable to fashion any clear chances before the break, Aaron Cresswell whipped in a dangerous free kick on the stroke of half time, but Kenny headed that behind confidently, and when the subsequent corner was cleared by the Everton defense, it was the home side who took a two goal lead into the dressing room at half time.
Responding to his team's dismal first half performance, Moyes acted quickly in an attempt to bring his side back into the game with a half time substitution, bringing on Diafra Sakho in place of Pedro Obiang.
That change sparked the Hammers into life, and the visitors were very nearly level twice in the space of a minute. After Lanzini's thumping effort from 40 yards was beaten away by Pickford, West Ham reloaded into the Everton area, and Cresswell's curling effort from the left hand side cannoned off the Everton bar.
It was Sakho who then earned West Ham their best chance yet to get into the game on the hour mark, when, with his back to goal inside the Everton area, Ashley Williams slid in rashly and failed to get the ball, giving Michael Oliver no choice but to point to the spot for the second time in the match.
The responsibility of the spot kick fell to Manuel Lanzini, but Jordan Pickford showed just why Everton paid £30m for him in summer, getting down low to beat away the Argentinean's thumping penalty, and this time, there was to be no follow up on the rebound.
West Ham would live to rue that missed penalty in emphatic fashion just a few moments later as Rooney completed his first Everton hat-trick in stunning style.
Coming out of his area to deal with a harmless Calvet-Lewin flick on, Hart's clearance found Rooney just inside his own half, and the striker's first time effort flew over the despairing West Ham defende into Hart's unguarded net.
Unsurprisingly, that goal saw Everton return to the ascendancy, and a defense splitting move ended with Hammers captain Winston Reid limping off with an apparent hamstring injury as he stretched to block Calvert-Lewin's shot, and to rub salt into the wounds, the unmarked Ashley Williams headed the resulting corner passed Joe Hart to make it 4-0 to the now rampant home side.
The final, perhaps compulsory, act of the night saw Rooney receive a standing ovation as he was brought off to be replaced by Beni Baningime with five minutes remaining, having helped his side climb five points clear of West Ham in the final relegation place.