Jose Mourinho's side will play Young Boys and Valencia in their final two group matches, with qualification now firmly in their hands.
Statement wins away from home in the Champions League have been in short supply since Sir Alex Ferguson retired five years ago, but this was one. They are a fantastic team with an wonderful record at home.
A fortnight after being outclassed by Juventus at Old Trafford, victory at the Allianz Stadium represented a lot more than just a boost to United's prospects of reaching the Champions League knockout stages.
"Very important 3 points. and unbelievable support from the fans", the France global wrote.
However, after Paul Pogba was brought down slightly outside the area, United were offered the chance to get back on level-pegging.
Mata had been on the field six minutes, Marouanne Fellaini too, but they were inspired substitutions.
In the grand scheme of things, this was not, as Martin Keown put it, one of the club's greatest ever nights in Europe, but there were shades of the old United about it. Massimiliano Allegri chose to give Alex Sandro and Giorgio Chiellini a game off, saving them for Wednesday's game against United.
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In the scene, Prince William agrees with his brother, saying: "Yeah, I think it probably was a bit and I think it's a negative message".
The France worldwide was back in Turin in Wednesday as he took in a Champions League outing with the Red Devils.
Juventus seemed certain to be heading for all three points, with United struggling to carve out clear-cut scoring opportunities, but Mata hit a free kick into the top left corner in the 86th minute and that seemed to inspire Jose Mourinho's side. "It's a huge credit to the team for keeping on fighting and never giving up". I think Anthony Martial has been very important for them recently because he gives them the ability to get past players and supplies a finisher's touch up front.
You always think you have a chance in any game, even if you concede first, and also if you are not playing well - which is the way you could describe some of United's performances in the past few weeks.
Opposition doesn't come much tougher than Manchester City at the moment. "I was happy for the goal but disappointed because we should have won the game easily by three or four goals".
Whatever competition they are playing in, and whoever they are playing against, you just can not bet against them and I am always expecting them to score two or three goals.
"Today we did a big step, but it's not over yet."