The full-back received the ball from Bernardo Silva after a short corner and, with no Burnley players closing down, the Brazil worldwide unleashed an unstoppable right-footed effort into Nick Pope's top corner from 25 yards.
United were caught cold in a 2-0 defeat to Tottenham at Wembley last Wednesday, when Christian Eriksen put the hosts ahead in the first minute, leaving Mata relieved his side were able to respond at the first attempt.
Physio Ally Beattie was over-worked as he then had to revive goalkeeper Nick Pope after a collision with City captain Vincent Kompany as the visitors probed for the opening goal.
"They (City) are the top side in the division, but the energy the supporters brought today was absolutely fantastic and that's something that's changed over a number of years here".
Sterling missed another golden chance to score in the 71 minute when he got onto the end of a pin-point pass from Kyle Walker, but he fired inches wide of the target from just inside the box.
Danilo's first-half goal looked to put City well in control but following Sterling's big miss, Johann Berg Gudmundsson ensured that Guardiola's men rued their profligacy with an 81st-minute half-volley goal.
Andre Drummond makes All-Star team as injury replacement
BC-BKN-All-Star Game-Drummond, 95Drummond added to All-Star game in place of injured WallEds: APNewsNow. Sure, that strategy worked for Drummond, but that seems like a rare exception to the rule.
Still, this being City, they continued to pass their way through the Clarets back line, and created their best chance of the match only two minutes after Ederson's save. "We can't wait to play in front of our USA fans again".
Asked how he felt to accept the championship race is over in early February, Mourinho said: "It makes me feel that they [City] are doing so well that they are not letting the others come close".
David Silva became their latest injury victim in midweek and John Stones was again absent, having been ill recently, and so Guardiola named only six substitutes - a decision blasted by Sky Sports pundit Gary Neville. We have lost to these twice and done quite well, but we had to change something and went to two up front. We have to change something.
"We don't dominate too many games with the ball so we've got to keep our shape". We are in these positions all season.
"We had to dig in and do the ugly stuff".