City's victory was sealed by a memorable team goal from Ilkay Gundogan, the German finding the net after a 44-pass move to send his side two points clear in the standings ahead of Liverpool, which beat bottom club Fulham 2-0 earlier in the afternoon.
David Silva, scoring for the third straight home match for City, put Pep Guardiola's team ahead in the 13th minute after it had dominated the early proceedings against a lackluster United visitor missing the injured Paul Pogba.
Guardiola later said he was unhappy with his side -- "the first half was not so good" -- for failing to press home its advantage, but early in the second half came a second goal.
A one-two between Riyad Mahrez and Sergio Aguero saw the Argentina striker produce a fierce shot that David de Gea could not keep out in the United goal.
But United, excellent in midweek in shocking Juventus 2-1 in the Champions League,
showed fighting quality by responding with a 58th minute penalty by the in-form Anthony Martial after Ederson had pulled down substitute Romelu Lukaku in the box.
United kept in the match until the 85th minute when Gundogan provided the final touch on a mesmerizing move, handing the Red Devils a fourth league defeat of the season.
Jose Mourinho's team is left in eighth spot, 12 points adrift of its "noisy neighbor" that is on course to finish higher in the league for the sixth straight season since the legendary Alex Ferguson retired from the Old Trafford helm.
Mourinho blamed a draining week for the defeat. "We played two games away, difficult ones, where the second game was against one of the best teams in Europe," he added.
Liverpool, shocked by Red Star Belgrade in the Champions League in midweek, took the lead at Anfield in fortuitous fashion as Fulham's Aleksandar Mitrovic had a goal ruled out for offside which TV replays showed should have stood, only for the home side to break up field for Mo Salah to score his eighth of the season.
Kosovo-born Swiss international Xherdan Shaqiri, left out of the midweek trip to Serbia because of concerns of a hostile reception in Belgrade, scored the second after the break.
Later, Chelsea missed its chance to go temporarily top, but was held to a goalless draw by improving Everton at Stamford Bridge, while fifth-placed Arsenal escaped in a 1-1 home draw against promoted Wolves.