Chelsea, like the top two, remain unbeaten under Maurizio Sarri but lost ground in a goalless draw at home to Everton.
Arsenal also missed the chance to leapfrog North London rivals Spurs into fourth and needed Henrikh Mkhitaryan´s late equaliser to salvage a 1-1 draw with Wolves at the Emirates.
City remain two points clear of Liverpool, but open four-point gap on Chelsea.
A fourth league defeat of the season leaves United languishing in eighth, 12 points off the top.
Goals early in each half from David Silva and Sergio Aguero left City in a commanding position before an Anthony Martial penalty gave United hope of a comeback.
But Ilkay Gundogan put the result beyond doubt four minutes from time with a third goal that crowned a sublime 44-pass move.
"I think Man City right now and Liverpool, Chelsea, and even Arsenal and Tottenham, I think they have numbers to be champion, not just City. We´re just two points in front," said City boss Pep Guardiola.
"What is important is that we are consistent, that we play most of the time good, and always I see many things that we can improve."
´Fight for top four´United manager Jose Mourinho accepted his side are now just fighting to try and make the top four having finished second to City last season.
"Since the beginning of the season, we knew that our second position last season was a fantastic achievement for us, and this season we are going to fight for the top four," said Mourinho.
"To speak about the title you need to be in the top positions. So let´s fight to close the gap and jump into the top four, if one day we jump into the top four, we´ll see what the difference is."
United scored twice