But Romelu Lukaku ended his scoring drought against the league's top teams by levelling for United with six minutes left in the first half.
The chief architect of the Red Devils' victory was Romelu Lukaku, who scored a goal himself and set up another for Jesse Lingard in a fantastic fashion.
Jesse Lingard scored the victor in 75th minute of the second half to help Man United take a two-point lead over Liverpool. "The confidence just breeds (confidence) and we're ready for the next one. We showed our qualities and our desire in the second half".
Meanwhile, Chelsea boss Antonio Conte admitted his side were in danger of missing out on a top four finish in the Premier League after Tottenham moved ahead of them with a win at Crystal Palace on Sunday.
"It was a good, intense game to play in, with a bit of skill here and there, I think the neutral fan would have enjoyed it today", added Lukaku, who now has 13 league goals this season.
When you have these situations, you have to manage the game better and, with experience, with maturity, get three points.
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Team-mate Scott McTominay was again trusted by Mourinho in the centre of United's midfield and the 21-year-old recovered from failing to track Willian's run for Chelsea's opener to put in another effective performance.
Chelsea dominated the opening play with delightful football from their midfield, and they almost got off to a dream start on five minutes when Marcus Alonso swung in a risky cross, which reached Alvaro Morata, who from 10 yards out, struck a volley which came back off the crossbar.
The only visiting player to consistently trouble United players was Willian - a player often overshadowed by the more explosive Eden Hazard but, in many respects, just valuable for his mazy movement on and off the ball.
But what he also does now, for the winning goal, I've always felt he's just a goalscorer, there isn't too much more to his play, he's not great at hold-up at times and he doesn't work the channels, but this just answers me and plenty of his critics - there is more to his game.
"For some reason, they were the champions last season, for some reason they played the way they did against Barcelona, for some reason they start the game so well as they started here".
"We are disappointed with the final result", Conte continued.
After the game, the Belgium worldwide expressed his belief that he deserves a "a bit more respect" for his record this season.