Yakubu scored at Upton Park for the second time in a week
Everton proved too good for West Ham for the second time in three days to remain unbeaten in 12 games.
Yakubu, who sealed Everton's midweek Carling Cup win, headed home after good work from Tim Cahill and Mikel Arteta in the dying moments of the first half.
West Ham missed a host of chances with Dean Ashton volleying wide and Freddie Ljungberg seeing a shot blocked.
And Andy Johnson sealed the win deep in injury time, catching keeper Robert Green off his line.
West Ham were eager to avenge Wednesday's 2-1 Carling Cup quarter-final defeat and driven forward by Scott Parker, they created plenty of goalscoring opportunities before Yakubu broke the deadlock moments before the half-time whistle.
Parker was at the centre of all West Ham's moves going forward, most notably setting up Ashton's looping volley which drifted just wide of Tim Howard's goal midway through the first half.
Ljungberg should have also done better but had his shot blocked after failing to make the most of a one-on-one with keeper Howard.
But against the run of play, Everton gained a crucial edge when Arteta picked out Cahill in the Hammers box and the Australian headed back across the goal to leave the unmarked Yakubu with an easy nod past Green.
It was only Everton's second clear chance of the half - the first came when Leon Osman found space on the edge of the Hammers box but slipped as he struck the ball and it sailed harmlessly over.
West Ham were forced into a change at the start of the second half with Henri Camara on for the injured Carlton Cole.
Parker continued to provide the spark in midfield but Everton, buoyed by their lead, showed more attacking intent and Lee Carsley unleashed a dangerous long-range effort towards the top right-hand corner of the goal, only to see it deflected wide.
Osman was left to rue a missed opportunity when he was sent through into a one-on-one with Green but knocked the ball wide, while a drive from Yakubu from the edge of the box was parried away.
Everton were forced to weather a late barrage, with West Ham keeper Green moving towards the halfway line to help hoist the ball into the box.
But the Toffees regained possession and took advantage of a defenceless goal as substitute Johnson lofted a shot over the retreating Green to secure victory.
West Ham boss Alan Curbishley:
"Where we were left wanting is that we needed to take that first chance - we had a glorious couple of chances and didn't take them.
"We've had two tight games with Everton but they've been closer than the scores suggest. I think Everton's first goal on the stroke of half-time was a blow.
"But the second half, we gave it our best shot but didn't have the quality to break them down."
Everton boss David Moyes on Yakubu:
"It probably shouldn't be a surprise to him that he's a leading goalscorer.
"He scores goals, he gets in the right position and his play has been really good - he's linking the team up and his work-rate is excellent.
"We think we've got good players, a great football club, and we're trying to make strides in the Premier League."
West Ham: Green, Neill, Collins, Upson, McCartney, Solano (Noble 59), Parker, Mullins (Reid 79), Ljungberg, Ashton, Cole (Camara 46).
Subs Not Used: Wright, Spector.
Everton: Howard, Neville, Yobo, Jagielka, Lescott, Arteta, Osman, Carsley, Pienaar, Cahill, Yakubu (Johnson 87).
Subs Not Used: Wessels, Hibbert, Gravesen, McFadden.
Booked: Yakubu, Johnson.
Goals: Yakubu 45, Johnson 90.
Ref: Steve Tanner (Somerset).