With City boss Manuel Pellegrini and his United counterpart David Moyes taking charge of their respective sides for the first time in the Manchester derby, it was the Chilean who emphatically came out on top.
Sergio Aguero volleyed home superbly to cap a flowing move after 16 minutes as the home side made their early dominance pay.
United, who were without the injured Robin van Persie, slowly came back in to the game, but were caught out in first-half injury-time as Yaya Toure doubled City's lead from a corner.
Aguero's second and a volley from Samir Nasri within the opening five minutes of the second half killed off any hopes of a revival for Moyes' side.
Wayne Rooney became the all-time leading scorer in Manchester derbies with a fantastic late free-kick, but it was City's day as their memorable victory took them up to third place.
Earlier in the day Arsenal picked up a 3-1 win over Stoke at the Emirates Stadium to return to the top of the table.
Club-record signing Mesut Ozil had a hand in all three of the Gunners' goals as they eased past Mark Hughes' side.
The Germany international's fifth-minute free-kick was parried into the path of Aaron Ramsey, who helped himself to his seventh goal of the season.
Geoff Cameron then levelled for the visitors before Ozil's corner was turned home by Per Mertesacker to give Arsenal the lead at the break.
Bacary Sagna added a third from yet another Ozil set-piece to wrap up the three points with 18 minutes remaining.
Tottenham left it late to find a winning goal and overcome a spirited Cardiff side 1-0 in south Wales.
Having dominated the match for large periods, Spurs boss Andre-Villas Boas must have thought his luck was out as his expensively-assembled squad struggled to find a way past an inspired David Marshall in Cardiff's goal.
But two of Tottenham's summer signings combined in injury time as Erik Lamela's pass was tucked away by Paulinho to give the visitors the win and take them behind north London rivals Arsenal in the table.
Meanwhile, Swansea followed up their impressive Europa League victory in Valencia with a comfortable 2-0 win at Crystal Palace.
Michu needed just 80 seconds to open the scoring for the Swans, who went on to control the game and secured the win when Nathan Dyer fired in a second three minutes after half-time.