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The visitors threatened within the first 30 seconds as a slip from Mehdi Abeid allowed Wayne Rooney to put Angel di Maria through on goal, but Fabricio Coloccini was able to get back and clear things up.
Man Utd continued to push forward following that minor setback and, on the quarter-hour mark, saw Marouane Fellaini fire a shot into the Newcastle defence, with Ander Herrera's follow-up flying narrowly wide.
Rooney nearly opened the scoring in the 27th minute when he collected Young's ball before lofting a chip over Tim Krul that floated wide of the post.
Not long before the break, Papiss Cisse brought the ball down well before letting up from distance with a shot which flew a yard or so wide in the end.
After the restart, Marcos Rojo struck a ferocious shot from the edge of the box, but the ball was off target by about four inches.
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Just two minutes later, David de Gea had to be at his best to deny Riviere after the Frenchman latched on to Coloccini's headed flick-on.
There was no let-up to the action as Krul pulled off a smart double save from Fellaini and Young, while just before the hour Rooney had the ball in the back of the net, though it was disallowed for offside.
In the 65th minute, St James' Park erupted into applause as Jonas Gutierrez entered the pitch in a black-and-white shirt for the first time since beating testicular cancer.
Both sides continued plugging away as Cisse made the most of Herrera's hesitation to drag his shot wide of goal, while at the other end, Rooney tested Krul again.
Just as it seemed like both sides would play out a goalless draw, Young made the most of Krul's spilled ball in the 89th minute to poke home and break Newcastle hearts.
The result means that Man Utd remain fourth in the Premier League table and continue to mount a challenge for the Champions League places, while Newcastle remain 11th.