United maintained their 100 per cent record in the competition with two games to spare and a guaranteed top-spot in group H.
Despite being wasteful in the first half and a goal down after five minutes in the second period, United came back yet again to emerge winners against the Portuguese.
Alan, Braga's 32-year-old captain and scorer in the reverse fixture, opened the scoring from the spot, smashing past David De Gea in the 49th minute. United had no answers in the rain-hit match until the 80th minute.
For the nth time, Robin van Persie came to rescue United, scoring from more than 35 yards out with 10 minutes left after Braga goalkeeper Beto rushed out to clear the ball and failed to get back to his position.
United were soon winning with a penalty awarded to Wayne Rooney who didn't disappoint after missing the spot-kick against Arsenal.
Javier Hernandez gave a two-goal advantage for the visitors with a close finish during injury-time.
United fought their way back after manager Ferguson made tactical changes to bring in Van Persie for Danny Welbeck and Nani for Rafael. The game was also delayed for 12 minutes due to a power cut after Braga went ahead.
Van Persie has now scored 10 goals for United in 13 appearances.