Louis Saha's late winner against his former club Fulham gave Everton their first home Premier League win of the season after 87 minutes of frustration.
Marouane Fellaini did hit the post for the Toffees in the 27th minute but the home side struggled for any creativity.
Fulham should have scored in the second half but Zoltan Gera crashed his close-range header against the bar.
But substitute Saha soared high to head in his first goal for the club from Leon Osman's dangerous cross.
Everton, with the worst home record in the Premier League coming into the game, were up against a side with the worst away record in the top division and, despite midweek wins for both clubs, a lack of cohesion and confidence was immediately evident.
The first clear chance came in the ninth minute when Mikel Arteta found space down the left and chipped in an accurate cross only for Steven Pienaar to head weakly into the arms of Fulham keeper Mark Schwarzer.
Pienaar, whose passing generally was far too loose in the first half, did hit a great ball over the top for Yakubu to chase but the Nigerian was caught napping and failed to capitalise.
Jimmy Bullard did start releasing a few probing balls for Bobby Zamora and former Everton striker Andy Johnson - making his first return to Goodison - to chase, but overall it was a frustrating stalemate in the middle of the park.
The crowd were roused, however, after 27 minutes when Yakubu bustled towards the penalty area and, as the ball broke free, Arteta laid it off for the Toffees' £15m club record signing Fellaini.
606: DEBATE
Fulham did carve an opening when Bullard's dangerous cross caused Zamora and Everton keeper Tim Howard to clash.
As a result the ball broke free six yards from goal but Johnson hesitated and the goal-scoring opportunity was gone in a flash.
After a first half characterised by a lack of creativity and invention, the second started a little better.
Tim Cahill should have broken the deadlock when Arteta worked an opening down the left and stood up a superb cross but the spring-heeled Australian international headed just over.
Fulham were inches away from taking the lead when Gera crashed a header off the underside of the bar after Zamora had dinked a decent cross back across the box.
Everton boss David Moyes sought to increase his side's attacking threat by bringing on former Manchester United striker Saha in place of Fellaini with half an hour remaining.
But while Everton pressed with greater urgency, Fulham had the best chance when Bullard's 25-yard curling free-kick was palmed out by Howard before Zamora scuffed his rebound against the post.
Moyes made more changes, first bringing off the misfiring wide man Pienaar for striker Victor Anichebe, then replacing Yabuku with James Vaughan.
And he was rewarded four minutes from time when Osman whipped in a tantalising cross for substitute Saha to rise high and head powerfully past Schwarzer to leave Fulham still searching for an away win in the Premier League this season.
Everton manager David Moyes:
"It wasn't a good performance but the result was really important to us, that's two wins in a week now.
"It was always going to be tight, Fulham don't concede many goals. We've kept another clean sheet but we needed a bit of good fortune at times.
"We were a bit wasteful at times in the first half but in the end we got there."
Fulham boss Roy Hodgson:
"It's always tough to lose in the last five minutes and we missed two very good chances through Zoltan Gera and Bobby Zamora - it would have made a big difference if we'd taken those chances.
"It was a cruel fate. We had players around the ball and could have got closer to the cross I thought, but it was good movement in the box from Saha.
"When your team do well you should be congratulated on getting something from the game - even if it's only a draw - but to go away with another odd-goal defeat is a bitter pill to swallow."
Everton: Howard, Neville, Yobo, Jagielka, Lescott, Arteta, Osman, Fellaini (Saha 61), Pienaar (Anichebe 76), Cahill, Yakubu (Vaughan 84).
Subs Not Used: Nash, Hibbert, Baines, Rodwell.
Goals: Saha 87.
Fulham: Schwarzer, Pantsil, Hughes, Hangeland, Konchesky, Davies (Nevland 89), Bullard (Baird 83), Murphy, Gera (Dempsey 88), Zamora, Johnson.
Subs Not Used: Zuberbuhler, Gray, Stoor, Andreasen.
Att: 31,278
Ref: Lee Mason (Lancashire).
BBC Sport Player Rater man of the match on 90 minutes: Fulham's Jimmy Bullard - 6.47 (on 90 minutes).
Please note that you can still give the players marks out of 10 on BBC Sport's Player Rater after the match has finished.
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