Fabio Eiendrighi scored twice in the second 45 minuets to put Chelsea on the board.
That put the Blues 1-0 ahead at the break.
They then claimed another two with 10 minutes remaining as Andre Schurrle and Eden Hazard scored the winner and Andre Schurrle’s penalty sealed the win.
Chelsea manager Jose Mourinho: “I will remember this. We showed great determination in doing something we wanted, coming at them and scoring the first goal.
“We also deserved that, of course they are a young team and playing at home. We didn’t play with much possession, it was more of a fight.”
Media playback is not supported on this device Mourinho praises Man Utd players and fans
Manchester United manager Jose Mourinho: “They showed great patience and determination which is very much appreciated because it’s the first time that they’ve played up here.
“The difference between us and them was that they didn’t go after players all day – they came at us and were aggressive. I have to say they were better than us before the game.”
Manchester City goalkeeper Ederson made two excellent saves to deny Hazard from close range in what Mourinho described as a “very, very, good” performance.
His performance for City was his best since his first appearance for the English champions in a 4-0 win in March last season.
With the result, Mourinho’s side remain second.
What it means
Chelsea have now won two in a row in the Premier League for the first time since their fifth league match under Mourinho: last weekend’s 2-2 draw with Arsenal – their home defeat by Arsenal had been the first since they won five in a row in March 2014.
Jose Mourinho says the team’s performance after the defeat of Arsenal will help them in the remaining matches
The Blues improved from the first leg, going into the second at Emirates Stadium in dominating form, before finally falling to defeat – first by their arch-rivals Man City, then again at home by Manchester United.
How it happened
Both Chelsea and Manchester United, who both beat Chelsea in the 2013 FA Cup final, played with one goalkeeper, David De Gea.
City, though, played with three – with goalkeeper Joe Hart keeping one, David Silva keeping the other and Manuel Neuer keeping the third.
Chelsea started with