West Ham United fought bravely for an hour with ten men but eventually Everton's superior numbers told at Goodison Park on Saturday.
It had all looked so promising when Radoslav Kovac got his first goal for the club with an absolutely stunning long-range strike after 24 minutes. The game was then turned on its head eight minutes before half-time when James Tomkins was sent off for felling Tim Cahill in the penalty area. Luis Saha tucked the spot-kick away. Joseph Yobo gave Everton the lead three minutes after the interval before Saha got a simple third in the 77th minute.
The lineup showed one change from the Liverpool match seven days previously. Jack Collison made his first start since dislocating his kneecap against Wigan Athletic on 4 March. There was further good news as Carlton Cole was fit enough to return to the substitutes' bench.
Before the game, Lucas Neil led the players in throwing their specially-made T-shirts saying 'Thanks for the support' into the away crowd and the skipper and his team-mates then set about trying to reward those fans further by securing a result that would see them venture on European travels next season.
Everton, though, were keen to ensure that their last home game before the FA Cup final ended in their favour and had several speculative efforts on Robert Green's goal in the opening ten minutes. The Toffees then had their first clear sight of goal 13 minutes in when the big-haired Marouane Fellaini cushioned a Lars Jacobsen centre to Leon Osman, but he sliced the good opportunity wide.
West Ham edged their way into the game and a long ball over the top from Kovac sent Diego Tristan running into space. He bought the ball down, but Tim Howard was out quickly to narrow the angle and shepherd the ball out for a goal-kick.
The Spanish striker was involved again moments later when he showed some neat footwork to side-step his marker, but sadly he could only fire high into the crowd behind Howard's goal.
Kovac then gave the Hammers the lead midway through the half. There seemed little danger when the Czech international picked up a short pass from Mark Noble 35 yards from goal. But the midfielder had already seen an opportunity to unleash an unstoppable right-footed drive that flew past the stunned Howard.
The game-changing moment arrived 13 minutes later when Tomkins appeared to clip the on-rushing Tim Cahill in the area. Referee Phil Dowd swiftly showed Tomkins the red card and Saha dispatched the spot kick into the bottom right-hand corner of the net
Zola sought to re-organise his side with the introduction of Jonathan Spector and Cole at the interval with David Di Michele and Tristan making way. It was to no avail, though, as Everton took the lead just three minutes later.
Yobo controlled a deep Steven Pienaar corner at the far post before drilling a low shot past Green and three West Ham players on the goal-line. The hosts then nearly put the game to bed when Saha crashed a header against the outside of the post.
Just before the hour mark Spector was cautioned for remonstrating a little too strongly with Mr Dowd, before the man in black was the centre of attention again at the other end of the field.
The Hammers won a corner after good work from Cole. Noble floated it in and Upson headed the ball against Cahill's arm, but Dowd waved away the United players' screams for a penalty.
Zola's men continued to fight, backed by some vivacious support from the away fans and had two great chances within a minute of each other. First, Cole slipped Boa Morte through on goal with a perfect pass but the Portuguese could only fire weakly at Howard. Then, the returning England striker had a great chance of his own, but his touch when bringing down a long ball in the area was just a little too heavy and Howard gathered.
Both Zola and David Moyes made changes for the final 20 minutes with Junior Stanislas coming on for hamstring victim Kovac and Jack Rodwell entering the fray for Fellaini. Stanislas nearly made an instant impact when he ran at the backtracking Blues defence and fired in a driven shot that Howard gathered at the second attempt.
Everton got the killer third with 13 minutes to go. Pienaar did well to get past Spector on the touchline, before sending a dangerous low cross along the goal-line which left Saha with the most simple of tap-ins.
It could and probably should have been four seconds later, were it not for the heroics of Green, who first thwarted Saha in a one-on-one before clawing away a Cahill header from the top corner.
With the game seemingly wrapped up, Moyes made his final two changes with Saha and Cahill leaving the field and Jo and James Vaughan replacing them. Leighton Baines and Boa Morte both went into the book for fouls.
West Ham gave it their all, but had just a couple of corners to show for all of their effort as eventually their drive for European football ran out of gas - for this year at least.
They will, of course, be looking to end the season on a high when Middlesbrough visit the Boleyn Ground next Sunday when the winner of the Hammer of the Year 2008/09 will be announced.