David Moyes' men were desperate to open up some daylight between themselves and the bottom half of the Premiership table, but their task was made more difficult as Mikel Arteta, Phil Neville, Victor Anichebe and Simon Davies were all missing.
Everton welcomed prodigal son, Andy van der Meyde, back into the fold for his first start of the season, but the biggest cheer was reserved for the recovered Andy Johnson.
Hammers boss Alan Pardew arrived on Merseyside after guiding his side to a slender win over fellow strugglers Sheffield United. The East End club made just one change from that match with James Collins replacing Danny Gabbidon.
James McFadden, James Beattie and Johnson formed a three-pronged attack for Everton with Leon Osman and van der Meyde supporting them as Moyes' side signalled their intent to take the three points.
However, Carlos Tevez looked irresistible for West Ham and signalled panic in Tim Howard's area several times with Joleon Lescott and Nuno Valente realising they could be in for a difficult afternoon.
By the 15th minute it was end-to-end stuff with Johnson and Tevez causing problems for both sets of defenders.
Howard provided a breathtaking point-blank stop from Lee Bowyer after great work by that man Tevez, before van der Meyde reminded every Evertonian just what he is capable of a minute later. He turned Hayden Mullins and Paul Konchesky inside out before providing a wicked cross which Robert Green tipped away from danger.
Green saved the Hammers in the 28th minute when he palmed away a fierce Johnson drive, when the striker should have squared to an unmarked Beattie.
If everything for West Ham was moving through Tevez, then the same could be said of van der Meyde for Everton. He was enjoying an excellent return to the side, and Lescott will be wondering how he didn't score from the Dutchman's pin-point cross.
Moyes may have felt a little aggrieved that his side had not gone in a goal ahead on the ratio of chances created but West Ham were good value for the 0-0 half-time scoreline.
At the start of the second half a mistake by Johnson let in Tevez who passed to Anton Ferdinand and he saw his shot taken over Howard's crossbar by the swirling wind.
Seconds later Beattie spurned a good opening after being set up by Johnson's pass as he skied his effort into the Park End.
Beattie's fantastic run and pull-back helped Everton take the lead in the 51st minute. The former Southampton striker refused to give up the chase and managed to heave the ball into the Hammers area.
Jonathan Spector could only head the ball out to Osman who controlled it and fired his first goal at Goodison since April to rapturous scenes. It was the midfielder's 100th game for Everton.
McFadden should have put the Toffees two up a minute later but showed too much of the ball to Green.
Osman and Johnson both went close but West Ham were still dangerous with Tevez proving terrier-like in everything he did.
James Collins had a clean header on goal but directed it too close to Howard just past the hour mark and Lescott brilliantly blocked Tevez's screamer moments later.
Bowyer was lucky to stay on the pitch after scything down McFadden as the young Scot closed in on goal. Pardew replaced him with Teddy Sheringham seconds later and brought Marlon Harewood on for the anonymous Bobby Zamora as Everton started to control the game.
Van der Meyde made way for James Vaughan to a standing ovation and the teenager wrapped the points up in stoppage time with his first goal of the season.
McFadden won the ball and found Carsley who fed the ball to Vaughan and he fired his shot past a despairing Green after a great run.