Everton, who were without main striker Duncan Ferguson and then lost Paul Gascoigne with a knee injury after just five minutes, were an ordinary side made to look much better by a Hammers side found wanting in all departments.
Tomas Repka, who served his one game ban from the stand, could be forgiven for having second thoughts about his recent move and the experienced Czech international's return can't come quick enough.
All five goals owed much more to abysmal defending than anything special from the blue-shirted scorers, who ran riot in the second half at the expense of the hapless Hammers, who almost conceded two sloppy goals in the first two minutes of the game.
Yet ironically, West Ham should have taken the lead after 23 minutes when Sebastien Schemmel, Paolo Di Canio and Trevor Sinclair combined with a neat passing movement down the right flank. Schemmel, running on to Sinclair's pass, crossed low but Di Canio scuffed his effort wide of the far post from just six yards.
Hammers' only other real opening in an evenly-matched first half - in which the visitors had greater possession - fell to Frederic Kanoute, who volleyed over from a very tight angle.
If Everton's first goal, a header from Kevin Campbell on the stroke of the interval, came at a bad time, the second - seven minutes after the break - killed the game as well as Hammers' morale.
A simple inswinging free-kick from Mark Pembridge appeared to be dropping safely into the arms of Shaka Hislop until Don Hutchison inexplicably made an attempt to clear the ball inside his own six-yard box under no pressure from an Everton attacker and watched in disbelief as the ball looped into the net.
This was the start of the Hammers Horror show and what followed was not for the squeamish as a spate of misplaced passes, weak defending and a lack of spirit throughout the side opened the floodgates.
Danish midfielder Thomas Gravesen was allowed to run unchallenged from the centre circle before sliding in a low shot that deceived Hislop and found the bottom corner via the far post, full-back Steve Watson ran along the byline and collected a rebound from his own cross to slot past Shaka, and the misery was rounded off by Polish striker Thomas Radzinski, who skipped past Dailly and Hislop after Song's error and cut the ball in from an acute angle.
Although Glenn Roeder kept faith with his 4-4-2 formation until after the fifth goal went in, all three substitutes - Soma, Byrne and Kitson - were used to no effect.
The closest Hammers came to scoring their first goal from open play in four Premiership away games was a looping Kanoute header following Di Canio's chip just a minute after Everton scored their killer second goal.
The Italian received a warm ovation from the Goodison crowd, who remembered with affection his sporting gesture in the corresponding fixture last season, when he shunned a possible scoring chance to allow injured Toffees keeper Paul Gerrard to receive treatment.
But Everton, with Gravesen dominating midfield, showed West Ham no mercy and the east enders will quickly have to toughen up and show much more resilience away from home.
Former Hammers and Everton winger Mark Ward, working in the Goodison Park press box as a radio co-commentator, summed it up when he said: "I was very disappointed with the lack of desire from West Ham after they went behind."
It would be wrong to point the finger of blame at Glenn Roeder after today's showing. The Hammers boss picked his best available team, the attacking part of which tore Newcastle apart just six days ago, and can not be held responsible for the basic schoolboy errors and lack of passion that has been evident in the last two away games, at Middlesbrough and now Goodison Park.
Minute-by-minute:
1 - A long ball straight from kick-off causes confusion in the Hammers defence as Song misjudges the flight of the pass and allows Campbell to steal in behind him. The Cameroon defender recovers well to block the striker's effort.
2 - Alexandersson's right-wing cross is again poorly dealt with, as Radzinski pounces on the loose ball. Hislop dives bravely at the striker's feet to end the danger.
5 - Gascoigne is forced to hobble off after coming off worse in his challenge on Kanoute.
6 - Carrick's left-footed shot from 25 yards out rolls wide of the post.
9 - Substitution for Everton, Pembridge replaces Gascoigne.
14 - Pembridge's fierce left foot shot is deflected off Hutchison for a corner.
15 - Courtois plays a one-two with Kanoute and wriggles into the box before Xavier denies him with a well-timed tackle.
16 - Kanoute's cross is knocked back into the danger area by Sinclair and chested down by Hutchison for Di Canio, whose left-foot shot is deflected over for a corner.
22 - Pembridge picks up the ball in the middle of the field and advances towards goal before firing in a left-foot shot that Hislop safely palms over the bar.
24 - West Ham's best chance so far, as a flowing move out of defence sees Sinclair feed the overlapping Schemmel on the right, and the Frenchman's low cross falls perfectly for Di Canio, who slices his shot just wide of the far post.
31 - Radzinski's intelligent pass finds Naysmith unmarked at the far post, but the Scottish midfielder sees his shot blocked by Schemmel.
37 - Kanoute's speculative volley flies well wide of the target.
39 - Sinclair's chip into the box finds Kanoute, who spins and fires in a first-time volley that sails just over the bar.
44 - Hutchison's flick-on falls to Courtois, whose weak shot from 25 yards out dribbles wide.
45 - GOAL. Everton are giving too much time and space on the right and Alexandersson sends in a cross that Kevin Campbell gleefully heads past Hislop. Everton 1 West Ham United 0.
Added time: 3 minutes.
Half-time: Everton 1 West Ham United 0.
Second half:
49 - The Hammers defence back-off as Campbell flicks on a long pass but no-one tracks the run of Radzinski, who clips the ball past Hislop but wide of the post to let the visitors off the hook.
52 - GOAL. Everton double their lead in embarrassing fashion as a Pembridge free-kick from the right creates confusion in the six-yard box and rebounds off the feet of Hutchison into the net. Everton 2 West Ham United 0.
54 - Di Canio twists and turns on the edge of the area before clipping in a cross that Kanoute heads on to the top of the bar.
55 - Carrick finds Di Canio on the left but the Italian's left-foot shot is easily saved by Gerrard.
56 - GOAL. Things go from bad to worse as Gravesen is unbelievably allowed to run unchallenged from the centre circle before sending in a low right foot shot from just inside the area that deceives the Hammers defence and nestles in the bottom corner of Hislop's goal. Everton 3 West Ham United 0.
63 - Substitution for West Ham, Soma replaces Winterburn.
66 - Gravesen's dipping volley from 30 yards out is superbly tipped over the bar by Hislop.
71 - Di Canio's free-kick is met by the head of Kanoute, but the ball drifts just wide of the post.
75 - GOAL. Another poorly conceded goal as Campbell releases Watson on the overlap in the penalty area. The full-back reaches the byline and cuts back a low cross that Hislop only palms back into the danger area. Watson, carrying on his run, sidesteps the Hammers keeper and slots home. Everton 4 West Ham United 0.
76 - Substitution for West Ham, Byrne replaces Courtois.
79 - GOAL. It's a Hammers horror show as Song completely misses a through-ball and Radzinski skips past Dailly before rounding Hislop and cutting the ball in from a tight angle. Everton 5 West Ham 0.
80 - Substitution for West Ham, Kitson replaces Kanoute.
82 - Double substitution for Everton, Hibbert replaces Pembridge and Moore replaces Radzinski.
Added time: 2 minutes.
Full-time: Everton 5 West Ham United 0.
Report and reaction to follow.