© PA Photos
Van Persie should have given the Red Devils the lead on 11 minutes, but the Dutchman fired against the post after dribbling the ball around goalkeeper Tim Howard.
The deadlock was broken two minutes later, as Van Persie got the better of John Heitinga before squaring to Giggs, who tucked away from 12 yards.
United then doubled their lead in first-half stoppage time, when Van Persie passed the ball into the net after collecting Rafael's through-ball and once again rounding the goalkeeper.
Jonny Evans came closest to adding a third goal in the second half.
The Northern Ireland international was twice denied by Howard on the goal line, before Everton eventually cleared the goalmouth scramble.