Conte's men beat United 4-0 in the Premier League in October before knocking the Red Devils out of the FA Cup quarter-finals with a 1-0 home win in March, but Mourinho's side put on a superb display on Sunday despite Zlatan Ibrahimovic not starting.
Chelsea were without Thibaut Courtois (ankle injury) and Marcos Alonso (injured during the warm-up), and goals from Marcus Rashford and Ander Herrera either side of half-time decided a contest that the visitors were never really in to begin with.
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Chelsea starting XI: Begovic; Zouma, David Luiz, Cahill; Moses, Kante, Matic, Azpilicueta; Pedro, Diego Costa, Hazard
Subs: Eduardo, Ake, Terry, Loftus-Cheek, Fabregas, Willian, Batshuayi
Manchester United starting XI: De Gea, Valencia, Bailly, Rojo, Darmian, Fellaini, Herrera, Young, Pogba, Lingard, Rashford
Subs: Romero, Blind, Fosu-Mensah, Shaw, Carrick, Mkhitaryan, Ibrahimovic
WHAT THEY SAID
Antonio Conte: "I have zero problem [with Mourinho]. It's a sporting competition between me and him.
"There is a game of football and I want to win with my team, he wants to win with his team. It's normal to be in conflict during the game but only a sporting conflict.
"Do I like the conflict? No, I don't like it. I prefer to concentrate on my team. But sometimes it's normal for me and the other coach to have this situation. But do I like it? No."
Jose Mourinho: "They have a certain style of play. They stick to it, they do it very well.
"Not every team defends with 11 players and they defend with 11 players. Not every team is so objective in their counter-attacks.
"They are very objective in the counter-attack and they have individual players out of the context of the game that can also resolve the problems, so they are a very strong team."