Olivier Giroud recovered from a disappointing midweek performance against Monaco to give Arsenal a half-time lead over Everton with his goal shortly before the break.
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A quiet opening period saw Everton enjoy the bulk of possession, but there was little goalmouth action until Muhamed Besic fired well over following a strong run by Romelu Lukaku.
The Everton striker then stole the ball from Gabriel Paulista, but David Ospina's quick closing down prevented Lukaku from getting his shot away.
Paulista's nervy afternoon continued when his wayward header from the edge of his own box nearly fell for Ross Barkley, but Ospina was alert to the danger and rescued the Gunners.
Arsenal's first chance came when Giroud threw himself at Alexis Sanchez's near-post cross from the left, but the French striker could only send his header inches wide of goal.
Paulista then redeemed himself for his earlier errors with a perfectly-timed tackle on Lukaku as the Everton man looked set to pull the trigger following a surge into the Arsenal box.
With half time looming, Giroud followed his teammate's example when he made amends for his earlier miss by sweeping home the opener from Mesut Ozil's corner.
Joe Sharratt
