Alvaro Morata's 55th-minute header proved the winner for the Blues, who uncharacteristically dominated possession at Stamford Bridge.
They attempted 18 shots on goal and found the target eight times, from which they should have scored at least twice more.
Defeat for United was their second of the season and they're now eight points behind league leaders Manchester City, who are running away with the Premier League title.
Jose Mourinho's side lacked creativity at the bridge. Henrikh Mkhitaryan started in the No.10 role but had a very quiet game, which meant Romelu Lukaku and Marcus Rashford lacked service.
Indeed, Lukaku didn't touch the ball in Chelsea's penalty area once throughout the 90 minutes. Not once.
Chelsea were fully deserving of their victory, but according to Mourinho, the game was even and his side had plenty of chances.
"I think they scored a goal in the only period where they were on top of the game. It was even aside from that," he said. "With the first goal they then brought more people in to defend.
"I was on the bench following the game, not counting chances. We had chances. We had lots of chances to score a goal."
If you say so, Jose. Rashford had arguably United's best chance of the game when his header looped over Thibaut Courtois but fell onto the roof of the net.
Mourinho decided it was time for change in the 62nd minute when he brought on Antony Martial and Marouane Fellaini for Mkhitaryan and Phil Jones.
Jesse Lingard was then introduced with 12 minutes remaining, replacing Ashley Young, but something pretty embarrassing happened to the winger earlier in the game.
According to Manchester Evening News' Samuel Luckhurst (see below), Mourinho had ordered Lingard to start warming up moments before Chelsea's goal.
But when Morata found the back of the net to make it 1-0, Mourinho changed his mind, told Lingard to sit down and sent Martial out to get warm instead. Martial then came on minutes later.
Make of that what you will, but it sounds like Mourinho was more confident Martial would get United a goal back than Lingard. Awkward.
Neither player made a difference in the end, but Lingard's confidence must have taken a hit when Mourinho snubbed him in favour of Martial.