Svilar made history as the Champions League's youngest-ever goalkeeper at 18 years and 52 days, but his disappointing positional judgement resulted in Marcus Rashford scoring the decisive goal 26 minutes from time.
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 very bad position.
Rashford grabbed the victor in freakish circumstances on 64 minutes as Benfica keeper Mile Svilar carried his deep free kick over the line.
United, who did not qualify for the Champions League last season, now have nine points out of nine in Group A and look nearly certain to qualify for the knockout stages but Benfica, without a single point, have a mountain to climb.
Of course, Manchester United are lead by Jose Mourinho, who is known for his tendency to play conservatively on the road in the Champions League, especially when there isn't much at stake.
It took 15 minutes for the first flicker of quality to bring the first chance.
Ander Herrera drilled wide and Rashford had a hopeful effort when play resumed, with the latter soon showing exceptional skill to take Douglas off his feet out wide.
However, Rashford had found a chink in Svilar's armour and made it count from a free-kick out wide, catching the teenager out of position as the goalkeeper failed to stop the ball crossing the line.