Jadon Sancho scored his first Premier League goal after an absolute gift from Jorginho at Stamford Bridge.
United, who were without Cristiano Ronaldo, found themselves under the cosh for large spells against the Champions League winners but took the lead against the run of the play at the start of the second half.
The ball was cleared from a Chelsea corner and Jorginho attempted to trap the ball on the halfway line.
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However, the Ballon d'Or contender's touch was wayward and allowed Sancho to dart towards goal. The former Borussia Dortmund man could have passed to Marcus Rashford but instead kept his composure and coolly slotted past Edouard Mendy.
Sancho's strike was his second in a matter of days after he opened his account for United in the 2-0 Champions League win over Villarreal on Tuesday.
Sancho and United teammates celebrated passionately with the away fans in the corner after going ahead in surprise fashion.
Encouragingly for new interim boss Ralf Rangnick, United scored the goal after Sancho and Rashford got up the pitch quickly to seize on the error.
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Shortly after scoring in his second consecutive game, Sancho was replaced by Ronaldo by caretaker boss Michael Carrick.
Blues skipper Jorginho made amends for his mistake, however, when he sent David De Gea the wrong way with a typically calm penalty in the 69th minute.
The spot-kick was awarded by Anthony Taylor after an overly eager Aaron Wan-Bissaka clumsily kicked through the back of Thiago Silva inside the area.
Featured Image Credit: Image: Sky SportsTopics: Manchester United, Jadon Sancho, Premier League, Michael Carrick, Jorginho