West Ham United 0 Everton 2
Goals in the dying seconds of both halves from Yakubu and then substitute Andrew Johnson sent the Merseysiders into sixth place, as David Moyes' men extended their fantastic unbeaten league and cup run to 12 games.
But it would have been such a different story if Alan Curbishley's side had taken their early chances to avenge Wednesday's Carling Cup quarter-final defeat.
The Toffees last came unstuck against Liverpool in mid-October and having also made it into the last 32 of the UEFA Cup and those Carling Cup semi-finals, Moyes predictably named an unchanged side from the team that had ended the Hammers' dreams of Wembley in midweek.
Curbishley's side had only lost one Premier League game in their last seven outings, though, and although the East Enders boss had to make two changes as a result of injuries to Luis Boa Morte and Danny Gabbidon, their replacements Nolberto Solano and James Collins made a seamless entry into the side.
Indeed, right from the off, it was clear that West Ham were looking to avenge that cup defeat, as they took the game to Everton.
Tim Howard was quickly forced to palm Solano's difficult corner out from beneath his crossbar, while Dean Ashton bundled wide and then Freddie Ljungberg called upon the visiting keeper to make a point-blank stop.
Ashton cleverly connected with Lucas Neill's pinpoint pass, but his hook shot cleared both the advancing Howard and his left-hand post, while Scott Parker also headed into the sidenetting.
In reply, Leon Osman had mustered a couple of wayward shots but, in truth, Everton were posing little threat.
That all changed in the final moments of the opening period though when West Ham paid a heavy price for not taking those earlier chances, for the previously absent Yakubu muscled Matthew Upson out of the way to break the deadlock with a powerful, close-range header, after Tim Cahill nodded Mikel Arteta's deep pass back into the goalmouth.
Instead of being in front, West Ham now found themselves behind and they pitched on Henri Camara in place of Carlton Cole for the restart, before Mark Noble stepped from the bench to replace the unlucky Solano much to the anger of the home fans.
Hayden Mullins shot wide and Joseph Yobo made a last-ditch clearance from Camara, but West Ham just could not muster that elusive equaliser.
And as they pressed forward, they merely played into Everton's hands as the Merseysiders broke with pace, power and purpose.
The warning signs were there as Lee Carsley and Cahill both threatened Robert Green, who also tipped Yakubu's header away to safety, and as they pressed for one last time, Phil Neville's 93rd-minute clearance found substitute Johnson and he raced clear and lobbed the ball over the advancing Hammers keeper from 20 yards to seal victory.