Everton struck three times after the break to sink Sheffield Wednesday.
James McFadden opened the scoring after 59 minutes when he was brilliantly set up from close range by Yakubu.
And the Scot was on target again with six minutes left, with Yakubu again involved, finding Phil Neville to cross for McFadden to head home.
Yakubu got the goal he deserved after 85 minutes, taking McFadden's pass to race through and secure a place in the Carling Cup fourth round.
606: DEBATE
Everton suffered an early scare when keeper Stefan Wessels needed treatment to a head wound after a clash with former Goodison striker Francis Jeffers, but the German carried on after having his injury bandaged.
And he was largely untroubled in a desperately poor first 45 minutes, with Jermaine Johnson off target with three long-range efforts for Wednesday.
Everton stepped up the pace after the interval and McFadden and Yakubu demonstrated why manager David Moyes left England striker Andrew Johnson on the bench.
Deon Burton wasted a good chance to bring Wednesday level, but he wasted the opportunity and the threat of McFadden and Yakubu proved too much for the Owls defence.
Sheff Wed: Grant, Gilbert, Hinds, Wood, Simek, Whelan, Jermaine Johnson (Burton 67), Small, Kavanagh (Lunt 80), Tudgay, Jeffers (Sodje 73).
Subs Not Used: Burch, Bullen.
Everton: Wessels, Hibbert (Neville 46), Lescott, Stubbs, Nuno Valente (Baines 64), Jagielka, Pienaar, Osman, Carsley, McFadden, Yakubu (Anichebe 86).
Subs Not Used: Ruddy, Johnson.
Booked: Hibbert, Jagielka.
Goals: McFadden 59, 84, Yakubu 85.
Att: 16,463.
Ref: Rob Styles (Hampshire).
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