At half-time Chelsea had still not capitalised on their man advantage, but took the lead 6 minutes into the second half with a goal from Kanté.
United was without the suspended Zlatan Ibrahimovic, Wayne Rooney and Anthony Martial for the match and started with Marcus Rashford upfront.
Mourinho's second trip to his old stomping ground came on Monday night, with United contesting an FA Cup quarter final with his old side.
And Red Devils legend Ferguson did not look to be too impressed with what he was seeing in west London.
United had defended valiantly until that point, especially so David de Gea, but Chelsea's pressure inevitably paid dividends.
Mourinho is Chelsea's most successful manager and Conte spoke of his desire to emulate the self-proclaimed Special One last Friday.
United's only defeats since the 4-0 Premier League loss at Stamford Bridge - Mourinho's biggest Premier League defeat - were at Fenerbahce and Hull in competitions in which they still progressed.
Manchester United ace Phil Jones was spotted mocking Eden Hazard after the forward's "dive" which got Ander Herrera sent off against Chelsea.
United have gone for three at the back, with Ashley Young and Henrikh Mkhitaryan offering the attacking support to Rashford up top.
Indeed, only twice in their history have Manchester United had a longer winless run against a certain opponent (13 vs Liverpool in 1927 and 13 against Leeds in 1972).
Chelsea will discover after the game whether it will face Arsenal, Tottenham or Manchester City in the semifinals next month at Wembley Stadium.