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Marcus Rashford and Anthony Martial scored the goals for the visitors, who should have made the margin of victory even greater with a host of first half chances.
Nicolas Otamendi pulled a goal back to give City hope five minutes from time, but that was too little, too late for Pep Guardiola's men, who suffered a fourth league defeat in 16 games.
United remain eight points adrift of their neighbours, but move up to fifth and within five points of fourth-placed Chelsea to haul themselves back into contention for a return to the Champions League next season.
In the midst of another testing season for United, Ole Gunnar Solskjaer's men have often saved their best for the toughest opposition having beaten Tottenham, Leicester and Chelsea and been the only side yet to take Premier League points off Liverpool.
