Depleted Everton produced a display of defiance to make sure of a 2-0 Barclays Premiership victory over West Ham which looked unlikely for long spells of the Goodison Park clash.
The Hammers dominated long spells of the game, with Carlos Tevez producing his best performance for the east London club.
The Argentinian ran Everton's defence to distraction at times - but West Ham were punished for not making better use of his quality and wasting enough chances to have been comfortably ahead before Leon Osman cracked Everton ahead early in the second half.
By the time substitute James Vaughan drilled home the second goal in injury-time, West Ham must have been wondering how they finished this game pointless.
They should be concentrating on escaping relegation rather than worrying about whether new chairman Eggert Magnusson - decked in his West Ham scarf in the directors' box today - will turn them into a European power.
Training ground injuries robbed Everton of Phil Neville and Mikel Arteta, although striker Andrew Johnson returned after a hamstring problem.
But Everton were also without midfielder Simon Davies because of a family bereavement, and with Tim Cahill still out, Dutch winger Andy der Meyde got a first start of the season.
West Ham were without hamstring victim Danny Gabbidon, which gave James Collins only his third game of the season after a groin problem.
Everton's resources dictated that they play with two wide men, James McFadden and Van der Meyde, with Joseph Yobo at right-back and Osman in central midfield.
The swirling gale made conditions very difficult, but Tevez was producing a display of running, passing and shooting which underlined just why he is considered such a bright prospect.
He twisted and turned on the right to create a 20-yard drive for Hayden Mullins, which was charged down, while another piece of neat play from the Argentinian ended with Paul Konchesky seeing a low drive blocked.
Everton, facing the teeth of the gale in the opening period, had trouble clearing their lines and Tevez again caused trouble on the right before setting up Lee Bowyer for a six-yard sidefooted effort which Howard palmed over the bar.
It took Everton a long time to get a foothold in the game, but when they did their aerial threat - made even more unpredictable because of the high winds - started to trouble West Ham.
Robert Green palmed away a curling Van der Meyde effort and then rescued his team when with a plunging save after Anton Ferdinand failed to deal with a long clearance from Howard, allowing Johnson to race away and fire in a low angled effort.
But Tevez was soon back in the spotlight, cutting in from the left to see Howard beat away a fierce right footer. A couple of minutes later Howard had to pull down another, less dangerous, effort from the same player.
Tevez kept up his supply of opportunities in the second period, surging through on the right to lay on an opening for Zamora, which he hooked over from 18 yards.
But it was Everton who broke the deadlock in the 52nd minute after James Beattie chased a lost cause down the right.
The striker pulled back a cross which Jonathan Spector headed only as far as Osman - and the midfielder chested the ball down before firing it into the top corner.
Everton were quicker now in the tackle, stopping the flow from Mullins and Nigel Reo-Coker while forcing errors.
Osman almost punished a Mullins mistake, winning the ball and running at Ferdinand before firing in a low effort which Green blocked.
Osman and Bowyer were booked for fouls before West Ham attempted to wrestle back some control by sending on Marlon Harewood and Teddy Sheringham for Zamora and Bowyer. Everton responded with James Vaughan coming on for the tiring Van der Meyde.
Howard, however, needed to block a fierce Harewood effort, before Collins was booked for a trip on Vaughan - and McFadden followed him into the book for a foul on Spector, who was replaced by Javier Mascherano with seven minutes remaining.
And in the third minute of injury-time the result was sealed when Mascherano was caught in possession and the ball was fed by Lee Carsley to Vaughan, who raced away to fire home the second.
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