United's dominance in the opening minutes saw them have 66% possession, although they failed to create more than that Rooney chance.
Arsenal were struggling to involve their creative players in the contest, and Van Persie pounced on 27 minutes to open the scoring against his old club. Rooney's curling corner was met by the Dutchman and the ball looped in.
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The Red Devils continued on the front foot as the half progressed, and Rooney claimed for a penalty when he was barged over in the box, but the referee saw it differently.
Szczesny went down after a clash of heads with Phil Jones, but both men were able to carry on. However, Jones did receive a yellow card.
The second half began without much in the way of action, and although Mesut Ozil could have equalised, he could only find the side-netting from a good position.
Minutes later, Rooney had a big chance to extend United's lead. After Van Persie had failed to control the ball, it fell to Rooney, but the striker's shot drifted wide.
The Gunners began to put pressure on the hosts, but Arsene Wenger's team were unable to force an opening.
Bacary Sagna then whipped in a cross that got a slight flick off a United head to go out for a corner.
However, the Gunners were unable to find a way past the home defence, although again Sagna sent in a cross that missed everyone.