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United struggled to force a response following their goal and they were reduced to speculative efforts from distance against a stubborn Stoke defence.
Rooney made up for his earlier mistake before the break by escaping his marker to head in Van Persie's perfect cross.
The home side's attacking trio combined well before the break but Danny Welbeck crashed his effort against the crossbar from the edge of the box following an exchange of passes between Rooney and Van Persie.
However, the Dutch member of the trio did put United ahead on the stroke of half-time with a smart cured finish from inside the box.