Sir Alex Ferguson's side were in danger of an embarrassing defeat at the hands of the Portuguese minnows after two early goals from Braga captain Alan shocked Old Trafford.
But Hernandez sparked United's revival with his first goal before half-time and the Mexico striker bagged the winner with 15 minutes remaining after Jonny Evans equalised just after the hour.
Hernandez's heroics ensured United maintained their 100 percent record after three Group H matches and one more victory should be enough to guarantee their place in the last 16.
Yet, while Ferguson will be pleased by his team's gutsy comeback, the United manager must have been shifting uneasily in his seat as Braga became the latest team to expose the hosts' defensive frailties.
Ferguson opted to rest Rio Ferdinand and Patrice Evra, but he talked in his programme notes about the perils of underestimating the supposedly weaker teams in the competition and paid Braga due respect by fielding a strong line-up that featured Hernandez, Wayne Rooney and Robin van Persie in attack.
It seemed like Ferguson's players weren't listening to his warnings as sloppy defending allowed Braga to take the lead after just 90 seconds.
Former Newcastle midfielder Hugo Viana was given time to swing over a cross from the left and Alan got in front of Alexander Buttner to plant a fine header past United goalkeeper David de Gea.
For the eighth time in 12 matches, Ferguson's men would have to come from behind after conceding the opening goal.
Reflecting the growing belief that United have something of a soft centre these days, Braga manager Jose Peseiro had promised to go on the attack and his team were proving as good as his word.
Even so, it was still remarkable how easily Braga carved through the United defence to double their lead in the 20th minute.
Michael Carrick, once again playing as a makeshift centre-back, was lured out of position to the left wing by Eder, who beat his marker with a sublime flick before whipping over a cross that Alan, given too much space by Buttner and Evans, dispatched with a clinical low strike.
That stunning development finally seemed to shake Ferguson's team out of their lethargy and Hernandez reduced the deficit just five minutes later.
Shinji Kagawa was allowed to play on after a foul on van Persie and the Japan midfielder lofted a cross towards Hernandez, whose diving header was too powerful for Braga goalkeeper Beto to keep out.
United had all the momentum now and Hernandez had the ball in the net again, only to see his goal disallowed for a borderline offside call against Kagawa.
Ferguson's team weren't to be denied though. Portugal winger Nani came on for Kagawa at half-time and United put the visitors under intense pressure in the second period.
Van Persie whipped in a free-kick that needed a strong parry from Beto at his near-post and only a series of last-ditch clearances kept United at bay in the following minutes.
But United had never lost at home to Portuguese opposition and Evans ensured that record would remain intact when the centre-back scuffed home the equaliser at the second attempt after Braga failed to deal with van Persie's 62nd minute corner.
The only question now has whether United would be able to complete their stirring fightback with a winner. The answer was emphatically yes.
In the 75th minute, Tom Cleverley curled over a teasing cross and Hernandez, timing his run perfectly, found space to bury a bullet header past Beto.