The home side pressured early on and tested David de Gea with a couple of long-range shots that were saved well by the Spaniard.
Marc Albrighton tested De Gea again on 10 minutes with a well-struck volley, but it was kept out well.
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Three minutes later, Welbeck grabbed a second, latching onto Antonio Valencia's low cross to put the ball into the back of the net via the underside of the crossbar.
Wayne Rooney should have made it three on 29 minutes after being found by Valencia, but the striker dragged his effort wide.
Welbeck almost completed a first-half hat-trick after being played in by Valencia on 34 minutes, but the striker could only pull his shot wide.