By Chris Harris at Emirates Stadium
Arsenal are back up to third place in the Premier League after a slow-burner of a match brought three points for the Gunners - and redemption for Olivier Giroud.
The France striker suffered more than most when Monaco won here in midweek but he struck six minutes from the end of a quiet first half, rifling in a first-time finish from Mesut Ozil's corner.
It brought Giroud his ninth goal in 13 games and brought relief to an edgy home crowd at Emirates Stadium.
Tomas Rosicky added a late second from the edge of the box after David Ospina had done as much as anyone to secure the points, stopping Romelu Lukaku by unconventional means in the first half and with fine reflexes in the second.
Everton will consider themselves unlucky but Arsenal deserve credit for their character.
The home side lacked their usual rhythm but this win sees them close the gap on second-placed Manchester City to four points, after the champions lost at Liverpool earlier in the day.
SETTING THE SCENE
Arsene Wenger's side went into this game with a point to prove.
A run of 15 wins in 20 matches had brought domestic progress, but Wednesday's deflating Champions League defeat to Monaco changed the mood. The visit of Everton gave Arsenal an early chance to make amends.
Wenger had hinted at squad rotation for this game and he went for two changes - Gabriel for Per Mertesacker and Alex Oxlade-Chamberlain for Danny Welbeck. Santi Cazorla donned the armband in the continued absence of Mikel Arteta while Giroud kept his place up front.
Everton were direct rivals for a Champions League spot last season but they have found the going tougher this term - they began the game 20 points adrift of the Gunners. That said, Roberto Martinez's players were on a high after a rather more pleasant European experience in midweek.
The restlessness in the stands seemed to transmit itself to the players as a cautious, nervy first half unfolded.
Everton enjoyed plenty of possession but their rather ponderous build-up created little of note. Arsenal, to coin their manager's phrase, played with the handbrake on, no doubt a reaction to their midweek chastening.
In the fifth minute a fine inswinging delivery from Luke Garbutt was headed clear by Francis Coquelin under considerable pressure, before Muhamed Besic skied a first-time effort over Ospina's bar.
The Arsenal keeper came to his team's rescue in the 17th minute after Gabriel let a long ball to bounce. Lukaku stole in but Ospina stuck out a hand to avert the immediate danger and then executed a perfect slide tackle outside the box. If Ospina's timing had been off, he might have been too.
The home side had to wait until the 27th minute for their first opening. Cazorla injected some pace into a counter-attack and Ozil found Alexis for an early cross that Giroud did well to reach ahead of Phil Jagielka. Giroud's stooping header flew just wide - but the offside flag was up.
Either way, it got Arsenal going - on and off the pitch. Suddenly the passing was crisper, the tempo higher, the crowd noisier.
Hector Bellerin had a sight of goal 10 minutes before the break but Jagielka dived in to block. As the game belatedly opened up, Lukaku raced away down the right, but Gabriel made amends for his earlier mistake with a fine covering challenge.
The half ended gloriously for Giroud as he applied an instinctive first-time finish to Ozil's right-wing corner, and Cazorla almost added a spectacular second with a curling effort from the edge of the box.
Everton started the second half on the front foot and they were given extra encouragement when Ospina spilled Garbutt's free-kick. The resulting corner eventually fell to Gareth Barry, but his acrobatic effort flew over.
Kieran Gibbs headed another teasing delivery from Garbutt away from the near post as Everton pushed forward, and Kevin Mirallis saw two efforts blocked as the visitors applied more pressure.
That pressure was alleviated when Giroud shrugged off Jagielka to fire in a shot that hit the grounded Everton captain on the hand, and Ozil also had a sight of goal but missed the target with his long-range effort.
But Everton were largely in control, and Arsenal were once again indebted to Ospina when his fingertips thwarted Lukaku after the striker had met Ross Barkley's cross with a swing of his left boot.
A nasty-looking mid-air clash between Giroud and Coquelin left the latter needing attention, and when play resumed the visitors picked up where they left off. This time Seamus Coleman's cut-back found Lennon but Ospina got down to save his low shot.
Gaps were opening up on the break for Arsenal and Ozil almost sealed the win with a prodded effort from Oxlade-Chamberlain's pass which Howard diverted over.
Instead it was Rosicky who had the final word with a shot from the edge of the box which clipped a defender and found the net.
Referee: Andre Marriner
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