After Leon Osman had wiped out Carlton Cole's opener, the Nigerian striker seized onto a disastrous defensive mix-up between Danny Gabbidon and Robert Green to bag his tenth goal of the season and break Hammers' hearts.
Perched handily in seventh spot, Everton had arrived at Upton Park attacking on all fronts having both made it into the knock-out stages of the UEFA Cup and dispatched Sheffield Wednesday and Luton Town in the previous rounds.
And although the Merseysiders were forced to replace the injured Leighton Baines (hamstring) with Phil Jagielka following their weekend win over Fulham, they still had hat-trick hero Yakubu leading the line and, after the Merseysiders forced a couple of early corners, the Nigerian sent out an early warning with a stooping header that thudded just wide.
The Hammers - having already accounted for Bristol Rovers, Plymouth Argyle and Coventry City - came into this tie brimming with confidence too following their win at Blackburn Rovers on Sunday.
Alan Curbishley had made two enforced changes as Freddie Ljungberg and Ewood Park match-winner Dean Ashton replaced the injured Matthew Etherington (groin) and the cup-tied Nolberto Solano.
And having found their footing, it was the Hammers who warmed the frozen Upton Park crowd on just 12 minutes when the onside Cole cleverly controlled Lucas Neill's searching up-field pass, before rounding the lone-figure of the advancing Tim Howard and calmly rolling the ball into the empty net from 18 yards.
Although Tim Cahill scorched Green's gloves with a powerful 20-yarder, West Ham were well on top but they just could not unwrap the Toffees defence, while Luis Boa Morte and Ashton both blazed over from range.
Surviving that period of home dominance, Everton grew stronger as the half drew to a close.
Indeed, after the threatening Tim Cahill failed to make contact inside the six-yard box, the visitors finally levelled on 40 minutes when Steven Pienaar collected the ball at the back of the Hammers area, before patiently picking out Osman, who bagged his fifth goal of the campaign with a curling 12-yarder.
And the second half soon mirrored the opening period too as West Ham found goal chances few and far between, while David Moyes' men always looked threatening on the break.
With extra-time and possibly penalties looking odds-on, few would have bet on outsider Yakubu doing anything as he chased down Gabbidon and Green with just two minutes remaining.
But the Welsh defender and England keeper came disastrously unstuck as the Nigerian stole in between them to toe-poke the Toffees into the final four.