The victory - courtesy of goals from Bruno Fernandes and Luke Shaw - allowed United to leapfrog Leicester City into second place and cut Manchester City’s lead at the top of the Premier League to 11 points with 10 games remaining.
City were stunned 34 seconds into the encounter when referee Anthony Taylor pointed to the penalty spot after Gabriel Jesus brought down Anthony Martial just inside the box.
City goalkeeper Ederson got his right hand to the shot but it squeezed into the right hand corner to give the visitors the perfect start at the Etihad Stadium.
United doubled their lead when their goalkeeper Dean Henderson threw a quick ball out to Shaw who burst past two City defenders and after a swift exchange with Marcus Rashford, drove into the bottom far-corner.
Poor
"Obviously I don't think we started very well,” City midfielder Kevin de Bruyne told Sky Sports. “We knew it would be hard. We played into their hands with the first goal and we needed about 15 minutes to settle a bit.
“Then we played pretty good but we didn't score and that made a difference and made a mistake with the pressing for the second goal.
Despite the setback, Pep Guardiola’s side will remain favourites to usurp Liverpool as Premier League champions.
Earlier on Sunday, Liverpool lost 1-0 to Fulham at Anfield - their sixth consecutive defeat at home. Fulham remain in the relegation zone with 26 points but moved to within range of Brighton, Newcastle United and Burnley.
Liverpool have yet to win at home in the league in 2021 and the ambitions of manager Jurgen Klopp have turned from retaining their Premier League title into the dreary fundamentals of competition.
"To win football games, to win football games," lamented the German to Sky Sports. "So I don't have to stand and say we fight for this or for that. We have enough to do with fighting for three points."
