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Arsene Wenger's charges, however, were soon able to impose themselves into the game, Alexis Sanchez blasting a speculative long-range shot wide in the eighth minute, before Alex Oxlade-Chamberlain forced Black Cats goalkeeper Vito Mannone into a nervous spill minutes later.
On the quarter-hour mark, Danny Welbeck worked himself some room on the edge of the box before firing towards the top corner, but the ball ended up dipping just over the crossbar with Mannone well beaten.
The deadlock was broken by Arsenal in farcical fashion on the half-hour mark when Wes Brown played the ball back to his keeper, but the pass proved far too short, with Sanchez running onto it and lashing a chip over Mannone.
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Sunderland showed more intent at the start of the second half, culminating in an effort after 52 minutes as Sebastian Larsson's cross was met by Rodwell's head in the box. Wojciech Szczesny, however, was able to hold the ball.
At the other end, Sanchez fired an effort from 25 yards which beat every Black Cats defender, but the ball flew straight to Mannone.
As the game went on, the atmosphere on the pitch became increasingly heated as fouls and challenges flew in and several players were booked in quick succession.
Sunderland managed a rare effort on target in the 65th minute as Larsson picked up the ball in space and lashed in a fierce drive that Szczesny did well to hold on to.
The game opened up in the final 10 minutes, with Arsenal wasting several good chances and Gus Poyet's charges coming forward in a bid to find a goal.
The Gunners then doubled their lead courtesy of another mistake at the back, Buckley putting Mannone under pressure with a poor back pass and the keeper completely missing his clearance.
The gaffe allowed Sanchez the simple task of slotting the ball into the net for his second goal of the game.