The home side were thoroughly outclassed as goals from David Silva and Nicolas Otamendi extended City's lead at the top of the table to 11 points, with Marcus Rashford scoring a consolation goal for the Red Devils on the stroke of halftime.
They also ended Manchester United's run of 40 home games without loss in all competitions with a 2-1 win on Sunday.
People like videos so I've put the match highlights above, but this wasn't the kind of match that could accurately be summarized by a neat and tidy collection of each team's best chances. "We're going to see what will happen in January", Guardiola told a news conference on Tuesday.
He continued: "I am so happy because our job depends on if we win, so if we win we are so happy in our lives and in our jobs".
Yet the rotation made no difference to unbeaten City's relentless rhythm as they clocked up their 16th victory in 17 league matches this season, with only Everton having taken a point from them. We are so happy, we played really well - especially after the Old Trafford game.
The Belgian striker, who is alleged to have been heavily involved in the derby dust-up, headed in Juan Mata's 25th-minute cross and pointedly failed to celebrate.
Tottenham returned to the Premier League's top four as Serge Aurier and Son Heung-min were on target in a 2-0 win over Brighton at Wembley.
GETTY Luke Shaw is heading out of Manchester United
"I think it's fantastic for us", said Spurs manager Mauricio Pochettino. "And we miss an important player like Mendy". "I'm happy with the performance".
"Obviously, it's the same for every team but it's tough, it's hard and it's challenging, so we'll focus on the next game".
Arsenal dropped to seventh, a point below sixth-place Burnley, after a goalless draw at David Moyes's improving West Ham United.
The Hammers nearly completed a smash-and-grab in the end but substitute Javier Hernandez's shot from Mark Noble's pass hit the bar and bounced off the line.
It was undoubtedly a big game, in some respects a potential title-decider even though it came not even halfway through the season, and it made for great viewing as well.
Newcastle had Jonjo Shelvey sent off in stoppage time for two bookable offences.
After a couple of careless early passes gave Swansea some encouragement, City found their feet on six minutes through the recalled Sergio Aguero.
A brace by Japan worldwide Shinji Okazaki and a goal by midfielder Andy King gave the Claude Puel's side a comfortable away victory, as the Southampton's Maya Yoshida goal could not count for much.