Antonio Rudiger gave the Blues a first-half lead before Anthony Martial put United ahead with a brace in the second half.
The result means Chelsea go top of the table, at least temporarily, but United are still languishing in eighth spot, seven points off the pace.
Whether he enjoys it or not, Mourinho is the guy who is always portrayed as the villain of the piece, but there was so much more to this game than the incident with Ianni and his reaction to the fans who once idolised him.
Manchester United was on the verge of its most impressive win of the season Saturday at Stamford Bridge against Chelsea, but it didn't end how the Red Devils wanted and it resulted in some serious tension.
It would appear that a member of the Chelsea staff over-reacted (or at least that's how Mourinho feels) to the late goal. I understood that we were in the wrong side of the situation.
"I did not get respect back from Chelsea but that is not my responsiblity".
Yes, it wasn't his fault that Ianni celebrated so crazily in front of him, but there was little sense of Mourinho biting his tongue and refusing to take the bait.
"Sincerely, I have not seen [what happened], but I have spoken with Jose [Mourinho], then I have spoken with a member of staff because I think we were on the wrong side, so I have dealt with it immediately", he said. "We lost a lot of players in their national teams including Marouane Fellaini". Will Mourinho, a two-time former Chelsea manager, engineer another Stamford Bridge tactical masterpiece or will the intense criticism over his performance return after the two-week absence that was the worldwide break.
Sarri said that his side had been in control for the first hour but had then tried to pass the ball long rather than their usual style of conserving possession and building attacks. 'A physical match and United are better than us in a physical match. I prefer to play our football for 90 minutes.
"I am disappointed with the last 30 minutes", he told the BBC.