The Belgium star was touted as United's biggest threat with Wayne Rooney having to play a deeper role in the absence of Michael Carrick.
And Zouma was shifted into midfield to blunt his impact - which he did with great effect.
The Blues won through Eden Hazard's 38th minute strike, despite only having 30% possession.
He has scored a lot of goals so I had to keep an eye on him, and I think I did it well. I had to be physical with him and stay close to him
Kurt Zouma
And Jose Mourinho afterwards claimed his side dealt with Man United's danger men with perfection.
And the 20-year-old was pleased with his own role.
"I had to stay with [Marouane] Fellaini because we knew he is on fire at the moment," Zouma said.
"He has scored a lot of goals so I had to keep an eye on him, and I think I did it well.
Managers react after Chelsea beat Man United 1-0 [AMBIENT]
"I had to be physical with him and stay close to him.
"The game was very difficult. The most important thing was that we had one chance and we scored.
"We defended very well. Manchester United didn’t have many chances to score. We stayed compact."
Invalid email
We use your sign-up to provide content in ways you've consented to and to improve our understanding of you. This may include adverts from us and 3rd parties based on our understanding. You can unsubscribe at any time. Read our Privacy Policy
GETTY
Kurt Zouma on top of Marouane Fellaini
And the France under-21 international admits despite the 10-point lead at the top of the table the squad isn't getting ahead of itself.
"We have as much confidence as normal but we are very focused on the next game," he added.
"There is a long way to go and the season isn’t finished. We have to keep going."
