The hosts took the lead after just two minutes when Wahbi Khazri, on his home debut, curled over a free kick from the left that missed everyone and snuck in at the far post as United keeper David de Gea waited for a touch that never came.
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The Black Cats went into today's match without a win in 13 league games against top-half sides, but they were close to doubling their lead soon after the opener when Jermain Defoe managed to work a shooting opportunity in a crowded penalty area before failing to make contact with only De Gea to beat from close range.
Sunderland's early momentum was somewhat dented when Jan Kirchhoff had to be taken off injured after just a quarter of an hour and United soon grew into the contest.
It was another Mata attempt which led to the visitors' equaliser in the 39th minute. This time Mannone could only parry it out and Anthony Martial quickly reacted to the loose ball before dinking over the Sunderland keeper and into the corner from a tight angle.
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As in the first half, Sunderland were the better team at the start of the second and they had two excellent chances before the hour mark as first Defoe's goalbound flick was denied by Daley Blind's last-gasp block before Dame N'Doye, on his Black Cats debut, saw his low shot saved by De Gea.
United were struggling to create much in the second half as Khazri and Lamine Kone tested De Gea at the other end before the winning goal arrived in the 82nd minute.
The aforementioned January duo combined from a set piece, with Khazri's outswinging corner powerfully met by Kone, whose header could not be stopped on the line by either Martial or De Gea, who may be credited with an own goal after seeming to land on the ball and nudge it over the line.
United substitute Memphis Depay went closest to a late leveller when his rasping drive was beaten out by Mannone, with Sunderland defending well to see out the win and beat United at the Stadium of Light for the first time.
Sam Allardyce's side move up to 18th and above Norwich City for the time being and only one point behind North-East rivals Newcastle United outside the drop zone, while United stay fifth and they will drop to sixth should West Ham United beat Norwich later today.