The win, secured when the Spaniard darted between United centre-halves Chris Smalling and Eric Bailly, was just the reaction under-fire Blues boss Conte needed following a 3-0 loss away to Roma in the Champions League in midweek.
Chelsea more than merited the win and were it not for David de Gea between the sticks, the west Londoners could have been out of sight long before United finally applied some pressure at the death.
Tiémoué Bakayoko and Cesc Fàbregas both wasted excellent chances for the hosts while Manchester United struggled to work Thibaut Courtois, going closest when Marouane Fellaini's half-volley was pushed out.
We have broken down the game tactically and looked at where the match was won and lost.
Christensen shines in Luiz absence
The big team news was David Luiz being left out of the squad altogether. Conte was asked about the decision prior to the game and claimed it was a purely ‘tactical' decision.
It would have been easier to swallow had the Brazilian defender been dropped to the bench. But he was left out completely with 17-year-old Ethan Ampadu preferred amongst the substitutes. That suggests there was more to it than simply tactics.
Conte was vindicated in the end, though United had just eight shots in the game and two on target so it was hardly the sternest test of Chelsea's back three. Expect this one to rumble on until the Blues' next game at the very least.
However, the man to benefit from Luiz's absence was Andreas Christensen. The Dane returned from Borussia Mönchengladbach in the summer following a successful two-year loan spell in the Bundesliga – and has been hugely impressive since, often starting ahead of £30million summer signing Antonio Rudiger.
This was his third start in a ‘big' game having featured against Tottenham and Manchester City in the Premier League already. And again he caught the yet again, winning both the tackles he attempted, all four aerial duels and completing 85 per cent of his passes. On this evidence, Luiz will have a fight on his hands to get back in the starting XI.
Kanté frees up Fàbregas and Bakayoko
The other headline bit of team news from a Chelsea perspective was N'Golo Kanté's return to the starting XI. The all-action French midfielder was sorely missed in the Blues' last six games – not least Tuesday's 3-0 humbling in Rome.
And he quickly underlined his importance to Conte's side with his impact felt most keenly by Fàbregas and Bakayoko. Neither are defensive-minded midfielders and they have been ruthlessly exposed without Kanté – as well as the decision to sell Nemanja Matić to Manchester United without signing a replacement.
But against Matić and United, Kanté's presence enabled Fàbregas greater freedom to get forward and link the play. The Catalan was excellent against the Red Devils and was rightly miffed when he was substituted late on in favour of Danny Drinkwater.
Bakayoko didn't enjoy as big an influence on the tie as the man alongside him. But he was still important to securing victory, breaking forward and working box to box, as well as getting in some good goal-scoring positions. With better composure he might have had two goals in the first half.
Henrikh takes the Mkhi
The Armenian started the season in superb form, carrying on from the end of last season where he was integral in Manchester United's run to the Europa League final.
But it has been no secret that, in recent weeks, the former Borussia Dortmund man has been woefully short of his best. And that was the case once more at Stamford Bridge.
He wandered around for the first half looking lost; unable to get on the ball, influence the play or link the midfield to the forwards. And the upshot of his dismal display was two fold.
Firstly, Romelu Lukaku and Marcus Rashford were starved of service and unable to get in the game. Secondly, and decisively in the end, Chelsea's midfield controlled proceedings and gave the Blues the platform from which they were able to secure victory.
It was a wonder that it took José Mourinho until the 62nd minute to hook Mkhitaryan who had, by some distance, been the worst player on the field.
No repeat of Herrera heroics
When United beat Chelsea en-route to the Premier League title at Old Trafford last season Mourinho was rightly hailed for getting the better of Conte tactically.
The secret of the Portuguese's success that day was to issue Ander Herrera with a strict man-marking job. The workaholic Spaniard was shackled to Eden Hazard that day and stopped the brilliant Belgian from exerting his usual influence on the game.
But at Stamford Bridge Herrera was not assigned a man-marking role and was instead left to scuttle from place to place putting out fires. He got through plenty of work, but Hazard was influential as the Blues secured all three points.