Edin Dzeko started a crushing win inside 43 seconds with the first of his two goals, before the imperious Yaya Toure finished it in the 90th minute — with his 21st goal of the season in all competitions.
While City may now be installed as the favourite to go on and clinch a second league title in three years, United — the champion by 11 points last season — is guaranteed to finish with their lowest points haul in the Premier League era.
Sitting seventh and five points behind sixth place Tottenham, United is even struggling to qualify for next season's Europa League.
"I take responsibility for the team, I always will do," United manager David Moyes said, refuting suggestions his players aren't playing for him. "I don't think tonight was in any way a lack of effort or lack of commitment from the players, in fact I thought they were fully there but in some areas we didn't come up to scratch."
This was supposed to be one of City's toughest fixtures in a run-in that also includes matches at title rivals Arsenal and Liverpool. In truth, though, it will go down as one of its most routine wins of the campaign, with United outclassed from the first whistle and barely threatening City goalkeeper Joe Hart.
"Very delighted," City manager Manuel Pellegrini said, "because I think we played very well, not only attacking but also in defending."
With United struggling badly in Moyes' first season and its neighbour embroiled in the title race, Pellegrini raised the temperature in English football's northern hotbed by saying in February: "If we only consider this season, there is just one club in Manchester — and it is ours."
Not since the 1977-78 season has City held such a dominant cushion over United in terms of league points heading into a derby. It now stands at 15 points.
United, buoyed by two straight wins after the humiliating 3-0 home loss to Liverpool 10 days ago, has had to wait five weeks to actively reply to Pellegrini's taunt but City pressed home its superiority within a minute.
Rafael da Silva produced a tremendous last-ditch tackle on David Silva but City regained possession and after Samir Nasri dragged a shot against the inside of the post, Dzeko — fit after a bout of sickness — was on hand to bundle in the rebound for the quickest ever away goal in the Premier League at Old Trafford. United great George Best holds the record for the quickest goal in a Manchester derby — after 38 seconds in 1968.
The superb Silva and Dzeko wasted other great chances in the opening 20 minutes and United was lucky to reach the break with 10 men after Marouane Fellaini raised his elbow toward Pablo Zabaleta in the 30th.
The match ran the same course in the second half, with City showing much more class and composure on the ball, and Dzeko's second goal virtually ended the game as a contest.
It was simple in its execution, Nasri whipping an outswinging corner to the near post for Dzeko to guide a volley into the top corner. Rio Ferdinand was left trailing in the Bosnian's wake.
Moyes had a dilemma now — go for broke and risk being carved open like it was against Liverpool or tighten ranks and seek damage limitation.
In the end, he did neither and Toure drove a powerful strike across United keeper David De Gea and into the corner with seconds left in normal time, wrapping up a third straight league win at Old Trafford.
"We can't lose six homes games in a season and we have to put that right," United striker Wayne Rooney said, "and make this a place which teams fear again."