Here are the major talking points from the game.
The visitors struggled to get going at Old Trafford, though much of that was down to an excellent showing by Mourinho's side.
And Herrera, sent off in United's 1-0 FA Cup defeat at Stamford Bridge in March, doubled United's lead four minutes into the second half with a drilled effort from the edge of the box that clipped off Kurt Zouma and past Begovic, following good work from Ashley Young down the left-hand side of the box.
When put to Conte by Sky Sports that they understood the injury was sustained playing basketball for a commercial, Conte said: "I think it is not important now to understand the way that he had this injury".
Marcus Rashford, playing alongside Jesse Lingard up front, got the other.
Mourinho set his team up in a similar way when United fell to a 1-0 defeat at Stamford Bridge in the FA Cup last month after being reduced to 10 men following Herrera's red card.
"We knew that playing this way would be very hard for them".
"I think they deserved to win".
"'Well, obviously, they have beaten us two times and we don't want it to happen a third time", United star Paul Pogba said. It is mine. In this case I wasn't able to do the right motivation.
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"Against Crystal Palace we didn't deserve to lose, but today we deserved to lose the game. Courtois had an injury in the middle of the week and for this reason he wasn't available today, but I think it is right to focus on the game and not to find excuses". They are in good form and they have a lot of enthusiasm. "We must have the same".
Jose Mourinho made a decision to give Marcus Rashford a chance to start, and he certainly grasped it with both hands, scoring the opening goal as well. A constant menace for Chelsea's defense with his mobility and direct approach, Rashford ensured Ibrahimovic wasn't missed at Old Trafford.
"I was running with my hands next to my body and it was not my intention to touch the ball".
But it was Herrera who deservedly received the man-of-the-match award, for his first goal/assist combination in the same game since October 2015 against Everton, and for a magnificent man-to-man marking job on Chelsea playmaker Eden Hazard.
The Spain worldwide also contributed by doubling United's advantage with a deflected strike just four minutes after half-time.
He hailed his side's performance, adding: "It was nearly flawless".
"It was nearly ideal - you can not say it was flawless because you always have some things to improve", he said on Sky Sports.
"But I am really happy with the team and the results, because the Manchester City and Liverpool results on Saturday left us in the position of needing to win".
Mourinho added: "Maybe we didn't "rest" players ahead of Thursday [the Europa League second leg], we just chose the team we thought was the best team".
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