Belgian goalkeeper Mile Svilar, making his Champions League debut at age 18, was deceived by a long free kick taken by Marcus Rashford in the second half, going over the line while holding the ball with his arms outstretched in front of him.
But the youngster - who beat Iker Casillas' record to become the youngest keeper in the Champions League at 18 years, 52 days - took up an bad position.
Benfica captain Luisao was sent off in added time afer a lunge at United substitute Scott McTominay to compound the home side's misery.
Rashford grabbed the victor in freakish circumstances on 64 minutes as Benfica keeper Mile Svilar carried his deep free kick over the line.
Man United travel to Benfica in their third Champions League match of the season - and fans can watch it for free.
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Prior to that, Manchester United won 3 wins, twice was a draw and only once Benfica was stronger back in 2005.
It took 15 minutes for the first flicker of quality to bring the first chance.
There was a brief period of United attacking excitement before the break as Rashford and Henrikh Mkhitaryan missed the target either side of a Matic low attempt that Svilar dealt with - the only shot on target of a dire opening period.
Manchester United's own Andreas Pereira was said to be a serious consideration, but the Portuguese stopper stayed where he is, a decision he may reevaluate in the summer if other young goalkeepers continue coming to prominence around Europe.