The opening goal inside six minutes when the returning van Persie, who had not featured since mid-December, was on hand to nod home after seeing an initial effort kept out by Bluebirds keeper David Marshall.
Cardiff were able to work their way back into proceedings but that was put to rest just before the hour-mark when Young cut in from the left wing to send a well-struck attempt into Marshall's bottom corner.
The win was David Moyes' 12th in the league with United which took them to 40 points from 23 matches while Solskjaer's Cardiff remained at the foot of the table following a fourth-straight defeat.
2013/14 Barclays Premier League season scores
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