Yakubu struck a second-half hat-trick as Everton's excellent form continued at the expense of struggling Fulham.
Everton goal hero Yakubu celebrates his third goal against Fulham
The Nigerian bundled home the opener six minutes after the break when Fulham goalkeeper Antti Niemi could only block Tim Cahill's volley.
He headed in a second after 61 minutes, turning home Phil Jagielka's flick from Mikel Arteta's corner.
Yakubu added a brilliant third 11 minutes from time, curling in a precise finish from Steven Pienaar's pass.
It stretched Everton's unbeaten run to 10 games, the best sequence in boss David Moyes' five-and-a-half years in charge.
Everton restored Yakubu and Leon Osman to their starting line-up, with both Andrew Johnson and James McFadden dropping to the bench.
But it was Fulham who made the brighter start, forcing early corners, with Diomansy Kamara glancing one across the face of goal.
Goodison Park was saturated by pouring rain, making passing football almost impossible in the first half.
Everton did at least try to force the pace, and Fulham keeper Niemi saved well from Joleon Lescott and Arteta's deflected free-kick.
Boss David Moyes was forced into a reshuffle after 21 minutes when Everton full-back Leighton Baines pulled up clutching his hamstring as he raced down the flank.
He limped off to be replaced by Jagielka, who started at right-back then moved into central defence.
Everton broke the deadlock after 51 minutes in a fashion that befitted the scrappy nature of the game up to that point.
Cahill's shot was blocked by Niemi, but Yakubu was lurking to bundle the ball over the line.
Fulham almost replied instantly when former Liverpool midfield man Danny Murphy drove in a low shot which Everton keeper Tim Howard did well to turn to safety.
The game had opened up after the break, and Niemi was forced to make a fine stop from Osman's fierce drive.
Yakubu was on the mark again as Everton doubled their lead from a well-worked set-piece after 61 minutes.
Arteta's corner was touched on at the near post by Jagielka and the predatory Yakubu headed home from six yards.
Everton were a team transformed from their early struggles in the rain and were now producing some dazzling football.
And Yakubu crowned the victory with a brilliant strike to complete his hat-trick with 11 minutes left.
Pienaar was the creator with some fancy footwork, but Yakubu delivered the killer blow to curl a slide-rule finish past Niemi.
The Nigerian was then taken off, to a rapturous standing ovation from the Goodison crowd.
Everton manager David Moyes:
"Yakubu does what he does best - scored goals. He is getting better at the other things we want from him, but his strength is scoring goals and he's done it everywhere he has been.
"He scored three in the second half, and I think if we had scored six no-one could have questioned it. Some of our football in the second half was as good as we have played."
Fulham manager Lawrie Sanchez:
"It is difficult to cope with good quality players like Tim Cahill and Mikel Arteta, and Yakubu made the most of his chances.
"I know it sounds like whingeing again, but I thought the first goal was offside. It was another poor decision that went against us.
"It gave Everton a lift and formed the bedrock of their second-half display.
"We had to go forward from then, and that meant we could be opened up by a good side - and that is what Everton are."
Everton: Howard, Neville, Lescott, Yobo, Baines (Jagielka 23), Osman, Arteta, Cahill (Johnson 82), Carsley, Pienaar, Yakubu (McFadden 82).
Subs Not Used: Wessels, Anichebe.
Goals: Yakubu 51, 61, 79.
Fulham: Niemi, Omozusi, Hughes, Stefanovic, Konchesky, Davies, Davis, Murphy (Ki-Hyeon 74), Kamara, Kuqi, Dempsey (Healy 64).
Subs Not Used: Warner, Bocanegra, Baird.
Booked: Kamara, Omozusi.
Ref: Steve Bennett (Kent).