Kevin De Bruyne and Kelechi Iheanacho set each other up for goals in the first 36 minutes, during which Guardiola's City team gave a footballing clinic in passing and movement at Old Trafford.
Zlatan Ibrahimovic replied for United in the 42nd minute, volleying home after City debutant Claudio Bravo dropped a cross, to set up a thrilling second half of furious, end-to-end action during which De Bruyne struck the post.
Mourinho said United's "bad" first half cost his team. "What I told them at halftime was that for some of you, it looked like you are trying to do what I told you not to do," Mourinho said.
"Some of the boys, they felt the dimension of the game. Everything around the game: the derby, the big game, the focus, the attention. Some of the guys, they felt it."
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Guardiola greeted Mourinho with a handshake and a hug before kickoff. Then his team set about delivering a footballing lesson to United in the first half.
And much of it was instigated by a player jettisoned by Mourinho in the coach's days at Chelsea.
De Bruyne was at the heart of City's dominant start that showcased the team's technical prowess and movement that is the hallmark of Guardiola's teams down the years. Dovetailing with fellow playmaker David Silva in central midfield, De Bruyne kept finding space to hurt United with his strong running and through balls.
Wayne Rooney was among the United players looking off the pace and frustration got to the United captain when he gave Guardiola a little push as he attempted to take the ball off the City manager, who was holding onto the ball at a United throw-in.
De Bruyne was the provider for Iheanacho's goal, finding space in United's area to drift on to his left foot and drive a low shot against the post. The ball rebounded out to Iheanacho, a replacement for the suspended Sergio Aguero, to sidefoot into the net from six meters out.
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