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Arsenal kept themselves in the title hunt as they came from behind to win.
Leon Osman put Everton ahead when he exchanged passes with Steven Pienaar and converted at the near post.
Samir Nasri equalised with a low shot from 20 yards and Robin Van Persie headed Arsenal in front after Tim Howard parried Cesc Fabregas' shot.
With Arsenal then in the ascendancy, substitute Theo Walcott played a one-two with Abou Diaby before slotting in the third through Howard's legs.
It was a remarkable turnaround for Arsenal, who had looked far from assured at the start - largely because of their untried defence, which included debutant Mikael Silvestre in the centre.
With William Gallas and Bacary Sagna out, Arsenal were hoping their emergency line-up would be enough to keep out an Everton side that had won only once in their last eight matches.
But within nine minutes, the Gunners' backline had been breached.
Osman started and finished the move, passing the ball out wide to Pienaar before sliding in ahead of Silvestre to covert the South African's low cross into the box.
The goal sparked Arsenal into life and a superb ball over the top by Fabregas gave Van Persie the chance to restore parity but his volley was saved well by Howard.
But Everton refused to panic and on the counter attack they went close to doubling their lead when Osman's shot was deflected wide.
The visitors continued to defend with discipline and kept their shape as Arsenal attempted to raise the tempo.
Everton did well to clear a corner under strong pressure for Kolo Toure, who suffered a shoulder injury in the process and was unable to come out for the second half.
Joleon Lescott nicked the ball off Nasri's toes as he was set to score, while Van Persie smashed over when well places and later saw his free-kick punched away by Howard.
They might have paid for their misses when Lescott headed goalwards from a corner but Clichy was in the right position to chest the ball away.
Arsenal brought on Walcott at the start of the second half as Toure made way, and Arsenal reshuffled their defence in the Ivory Coast man's absence.
Perhaps sensing the need to protect an unfamiliar back four, Arsenal piled forward and quickly got the reward for their adventure.
Everton failed to completely clear a corner and Silvestre laid the ball of to Nasri to rifle in through a crowded penalty area and make it 1-1.
Van Persie then should have put Arsenal in front but smacked the ball high and wide from 12 yards.
Tempers flared soon after following a late challenge by Tony Hibbert on Denilson, and Clichy and Hibbert were both cautioned after squaring up to each other.
It seemed to unsettle Everton the most and it was not long before they fell behind.
Emmanuel Adebayor slid the ball to Fabregas and his shot was beaten out by Howard but only as far as Van Persie, who nodded home from eight yards.
Arsenal had been the superior team after the break, and Everton's lack of ambition cost them when they had looked good value for their lead in the opening half.
And the final word went to Walcott, who swapped passes with Diaby on the right flank before coolly slotting in the arsenal's third goal.
