The meeting took place in Manchester and ended in favor of the nominal guests - 2: 0.
In the second minute, Bruno Fernandes took United ahead from the penalty spot, and in the 50th minute Luc Shaw scored the second goal.
City's first defeat since December in the Premier League.
In addition, the 15-match winning streak of the Citizens was interrupted.
Manchester City tops the Premier League standings with 65 points.
Manchester United (54) are in second place.
Earlier it was reported that Liverpool was defeated at home by Fulham in the Premier League.