The win put them back in the hunt for a top four 2019/2020 English Premier League (EPL) finish.
In a high tempo, if often scrappy game, Ole Gunnar Solskjaer’s Manchester United side made the most of their chances.
But Chelsea, whose form at home has been suspect all season, squandered a string of opportunities.
A fine glancing header from Anthony Martial just before half-time from an Aaron Wan-Bissaka cross put the visitors ahead.
It was Manchester United’s first Premier League goal in four games.
Defender Harry Maguire made it two in the 66th minute, losing marker Antonio Rudiger to head home from a corner kick by Manchester United’s new Portuguese signing Bruno Fernandes.
Chelsea had two goals ruled out by the Video Assistant Referee (VAR).
Kurt Zouma scored from a corner kick in the 54th minute but there was a push in the area.
Substitute striker Olivier Giroud’s headed effort in the 77th minute was cancelled when he was adjudged marginally offside.
The loss left Chelsea fourth, a point clear of resurgent rivals Tottenham Hotspur led by their ex-coach Jose Mourinho and who they host on Saturday.
Manchester United, another of Mourinho’s old clubs, rose to seventh, three points behind Chelsea.(Reuters/NAN)