Chelsea saw their lead at the top of the Premier League cut to four points, after they were beaten 2-0 by Manchester United on Sunday.
Antonio Conte's men were hoping to restore the seven-point gap between them and Tottenham Hotspur, who hammered Bournemouth 4-0 at White Hart Lane on Saturday.
However, United who started with their top scorer Zaltan Ibrahimovic on the bench, took the lead in the opening 10 minutes.
Ander Herrera appeared to use his hand while winning the ball, before he released Marcus Rashford with a slide-rule pass. The teenager blasted the ball beyond Asmir Begovic, who was deputising for the injured Thibaut Courtois.
Jose Mourinho's men doubled their lead early in the second half, as Herrera's shot was deflected by Kurt Zouma and lopped over Begovic.