The away side were 1-0 down within 30 seconds thanks to some awful defending from Chris Smalling and Daley Blind, who allowed Pedro to round David de Gea and break the deadlock.
It would only get worse for Mourinho as Gary Cahill, Eden Hazard and N'Golo Kante capitalised on defensive errors to secure an emphatic victory.
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At the final whistle, Mourinho and Antonio Conte appeared to exchange a few heated words while shaking hands.
According to Gabriele Marcotti, per Sky Italia, United's boss said to Conte: "You don't wind up the crowd at 4-0. You do it at 1-0. It's humiliating."
The exact words Mourinho used has yet to be confirmed by either manager.
However, when asked about the incident, Conte did have a response and, after defending his behaviour, appeared to make a subtle dig at Mourinho's lack of a playing career.
He said, per the Mirror: "I was a football player, so I know how to behave on the pitch.
"There were United fans who kept singing, while ours were in silence after a great performance from my team. I wanted to call the crowd to applaud the players, which seems normal enough to me.
"I have great respect for everyone. Nothing happened with Jose, especially as my behaviour seemed normal. I didn't make fun of or humiliate anyone, as I always demand respect.
"Today, I think it is important to talk about the game and I say my players deserved this type of performance."
And so Conte should be allowed to rally Chelsea's fans. From defence to attack, the Blues were nothing short of sensational against United and fully merited their emphatic win.
It's slightly hypocrital of Mourinho to have criticised his Italian counterpart, too, considering how many times he's riled opposition managers with his own touchline behaviour.
The Portuguese was similarly asked what was said during his discussion with Conte but refused to divulge his exact words.
"It was with Antonio, not with you," he bluntly told reporters. "Of course not... I was speaking with Antonio, not with you. I am sorry."
Mourinho also discussed the reception he received at Stamford Bridge.
"Fine. I was not expecting anything different," he added. "The people inside the tunnel who are friends were friends, the ones that were not special friends were not special friends.
"The crowd behaved in a normal way so there was nothing wrong."