Alvaro Morata's header proved the difference for Chelsea as Manchester United boss Jose Mourinho left his former haunt Stamford Bridge empty handed.
Cesar Azpilicueta launched the cross into the middle of the box and found his striker unmarked in the box.
The Spaniard gratefully accepted the chance, heading into the top corner past his compatriot David de Gea for his seventh Premier League goal of the season.
The sides had gone into the break goalless but both had chances.
The Blues were perhaps the most unlucky, with an own goal from Phil Jones disallowed due to a foul by Morata.
Tiemoue Bakayoko and Marcus Rashford missed good opportunities, also, and Marouane Fellaini forced a good save from De Gea at the death.
Here is how John Cross rated the players' performances.
Chelsea
Courtois 7
Made a good save from Lukaku’s shot but generally United gave him a quiet game.
Azpilicueta 7
Played in back three then at right wing back and was rock solid in both roles.
Christensen 8
Was the supporting cast in the David Luiz soap opera. Looked calm and composed.
Cahill 7
Restored to the left of Chelsea’s back three and looked solid again. Good display.
Zappacosta 6
Steady performance at right wing back, bit got hooked when Conte tightened up.
Kante 9 (MOTM)
His non-stop performance showed how much Chelsea have missed him.
Bakayoko 6
Booked. His blue hair only drew attention to yet another average display.
Alonso 7
Very lively first half, drove forward and tried to make things happen.
Fabregas 8
Good passing, work rate and quality from Chelsea’s midfield dynamo.
Hazard 7
Lively and determined, but should have scored from big second half chance.
Morata 7
Fabulous header to put Chelsea ahead. Led the line with class and power.
Substitutes
Rudiger, for Zappacosta, 66 mins, 7
Drinkwater, for Fabregas, 78 mins
Willian, for Hazard, 87 mins
Manchester United
De Gea 7
The busier of the two keepers, made some smart saves. Excellent positioning.
Bailly 7
Tenacious and strong, he fights for every ball. Good in defence for United.
Smalling 7
Who says he can’t play? Did well in United’s defence and was good in possession.
Jones 5
Booked. Favourable decision from ref ruled out Jones’ own goal. Below par.
Valencia 6
Such a force at right back, he powered forward and showed strength in defence.
Herrera 6
Booked. Was an irritant in midfield, but offered very little going forward.
Matic 6
One of his less effective games. Did not boss midfield or get forward.
Young 7
Tenacious and determined, Young put in some dangerous crosses for United.
Mkhitaryan 4
Was awful. Completely anonymous. Again. Amazed he gets picked on this form.
Rashford 5
Had good early headed chance which he put over but was quiet overall.
Lukaku 5
Had one decent shot on the turn, but quiet overall. Morata proved his point.
Substitutes
Fellaini, for Jones, 62 mins, 5
Martial, for Mkhitaryan, 62 mins, 5
Lingard, for Young, 78 mins