A stunning Alvaro Morata header ensured another disappointing return to Stamford Bridge for Jose Mourinho.
The Chelsea striker rose to head home an excellent winner from Cesar Azpilicueta's cross. Substitute Marouane Fellaini came the closes to levelling the scores but he was denied by Thibaut Courtois late on.
Manchester United are now eight points adrift of leaders Manchester City, who saw off Arsenal earlier on Sunday. Here are five key talking points.
- Battle of the strikers
Both of the No9s could have ended up on the opposing side if their summer transfers had panned out the way they were expected to at the start of the close season.
In their first head-to-head since they both ended up where the other might have, Alvaro Morata won it hands down.
His soaring second-half header from Cesar Azpilicueta's cross – the fifth time they've combined for a goal - decided this match while and he constantly kept Manchester United's defender's occupied and on their toes.
For Romelu Lukaku this was another big game blank, though it wasn't for the want of trying.
There was no shortage of effort from the Belgian, running the channels and trying to compete aerially.
But he had just one sight of goal and it was far from a clear one, a shot from outside the box that was pushed away by Thibaut Courtois. - The Kante effect
How Chelsea have missed N'Golo Kante. In his first game back following a six game absence, in which the champions conceded 11 times, his impact was instant.
And it wasn't just what he brought to the team but the effect he had on his teammates.
Kante did what Kante did. Shielding his defence, stopping Manchester United in their tracks when they wanted to counter and being the first on the scene when the ball ran loose.
Of his teammates, Tiemoue Bakayoko seemed to benefit the most from knowing Kante was there to sweep up behind him.
The Frenchman was bombed forward all game to support match-winner Alvaro Morata and Eden Hazard and should have got his name on the scoresheet at least once. - Mourinho big game approach
It is not hard to see why Jose Mourinho prefers the cautious approach in the big away games.
His Manchester United team being more attacking might be better for the neutral but probably isn't for his heart rate.
They had much more attacking intent here than they have in most of his big away games as boss, playing with greater pace, intensity and two up front.
But the setup also left them more open, vulnerable to a Chelsea counter and they looked constantly on the verge of being opened up nearly every time the hosts poured forward.
Eventually they were when Alvaro Morata headed in Cesar Azpilicueta's cross to give Antonio Conte a victory to savour over his managerial rival Mourinho. - Luiz out, Christensen in
The Danish youngster was one half of Antonio Conte's biggest selection call, coming in for David Luiz who was dropped from the squad altogether.
It was the biggest test of Christensen's fledgling career and just his fourth Chelsea start.
You wouldn't have known it. Christensen was one of the coolest heads on the pitch and he played a big part in a much more solid display from Chelsea's regard.
The way he got the better of Romelu Lukaku in the air, on the ground and when things got physical, was hugely impressive too. - United's Hazard tactics
Once again, Jose Mourinho singled out Eden Hazard as Chelsea's man to stop at Stamford Bridge.
In last season's cup tie the plan fell apart when Ander Herrera was sent off after picking up a second yellow for fouling the Belgian.
At Old Trafford Herrrera did a man marking job on Hazard and totally snuffed him out.
Today, Eric Bailly spent the first half following him around but that pulled Manchester United's defence out of shape.
In the second half they resorted to trying to bully Hazard out of the game.
Phil Jones and Herrera were booked for fouling Hazard early in the first half either side of Nemanja Matic fouling him. Herrera caught him again later too.
But Hazard never shied away from the rough stuff and kept dusting himself down and running at United again until he was taken off just before full time.
