The 3-0 victory was a third in eight days for the treble winners but followed an uncharacteristically sub-par spell where they had suffered three defeats in four games.
That said, their worries pale in comparison to those of their near neighbours, and the gulf between the teams was amply demonstrated here.
Erling Haaland scored twice – the first a penalty and the second a towering header from a delicious cross from the influential Bernardo Silva – before he turned provider for Manchester-born Phil Foden to ensure the scoreline was appropriately emphatic.
The victory hoisted Pep Guardiola's side to within two points of leaders Tottenham with the season now 10 games old.
Silva, who put in a man of the match display, said: “It was good game for us. Apart from a few simple balls we lost we didn't give them much to counter. The first 30 mins of the second half we were really good. The way we pressed, what we lacked against Arsenal, we were fabulous.
“When we come to these places, like Anfield and Old Trafford, we know what teams are waiting for – for us to lose the ball and counter. It is about the build up, not losing simple balls and controlling the game and being slow in the first metres of our half and goal kicks. After then it is about breaking through to attack. It is never easy to come here to beat this team.
“It is definitely one of the best wins. To win 3-0 away with this crowd, I think it is definitely one of the best performances.”
United made three changes to the side that had beaten FC Copenhagen in midweek. Victor Lindelof and Jonny Evans came in at the back in place of Raphael Varane and Sergio Reguilon, while Christian Eriksen, instrumental from the bench against the Danes, replaced Antony in a rejigged midfield.
Guardiola, meanwhile, made wholesale changes from the side he fielded against Young Boys, reverting back to something more like his strongest side. That meant starts for Foden, Silva, Josko Gvardiol, John Stones, Julian Alvarez and Kyle Walker.
The first and the last of those names were involved as City crafted the game's first big chance as Walker headed Rodri's cross back across goal and Foden's own header caused a scramble in the United box with Haaland lurking.
United had shown some spirit in the early going but were on the back foot by the 20 minute mark, with the visitors on top, and soon an attacking set-piece yielded a penalty as Rasmus Hojlund pulled back Rodri. A VAR check confirmed the spot kick and Haaland routinely dispatched it.
Hojlund had a chance to redeem himself as he latched on to Foden's wayward pass but he couldn't get a shot away under pressure from the recovering Stones.
City's dominance resumed but they needed a magnificent save from Ederson to preserve their lead as Scott McTominay tested the Brazilian keeper with a crisp half-volley from the edge of the box.
Almost immediately, at the other end, Andre Onana outdid him as he soared across his line to repel Haaland's powerful header.
Those of a City persuasion needn't have worried, however, as they created a carbon copy of the chance early in the second half and this time Haaland buried Silva's cross.
As if to illustrate their local dominance, City's premier local boy snatched the third.
Rodri released Haaland and the Norse striker – on a hat-trick no less – squared unselfishly for Foden to steer home and leave hosts United downtrodden and dejected.