Braga had stunned their illustrious opponents with two goals in the first 20 minutes at Old Trafford. Brazilian Alan headed home inside 90 seconds and the Portuguese side crafted a second as Alan again slotted past David de Gea after fine work by Eder.
United's Mexico striker Hernandez quickly replied from Shinji Kagawa's cross, Jonny Evans equalised from close range in the 62nd and Hernandez headed the winner 15 minutes from time.
Hernandez has become a bit-part player for United with the arrival of Dutch striker Robin van Persie, but took his chance to impress on only his fourth start in all competitions this season.
"He is improving all the time. He trains magnificently and he has great enthusiasm," said United manager Sir Alex Ferguson.
"I must say he has got me thinking. I have got him, Wayne Rooney, Robin van Persie and Danny Welbeck, and I don't know what to do with them."
United, who have lost only one of their last 37 Champions League home games, have nine points from three matches and are poised to reach the last 16. CFR Cluj are on four after a 1-1 draw at Galatasaray, Braga have three and the Turkish side are bottom with one.
Despite Braga's blistering start, Ferguson said he did not regret resting defenders Rio Ferdinand and Patrice Evra with Sunday's Premier League clash at Chelsea in mind.
"No, we have to look at the big picture - Rio, his age and a big game against Chelsea on Sunday," said the Scot.
"We have got injuries and putting Michael Carrick back there is not the best but we had to do it.
"It's been the story of our season at home, starting badly and losing goals. We have had to rescue games and it is the front players doing that. We played some terrific football tonight but it is a concern losing the goals."
Braga, who bounced back from an opening home defeat by CFR Cluj to win at Galatasary in their last Champions League game, began in confident style, as befitting a team who had not lost on their last seven European away games.
ALAN DOUBLE
Ferguson had barely settled into his seat when Hugo Viana whipped over a cross from the left and Alan got in front of Alexander Buttner, playing in place of Evra, to head into the bottom corner.
United then found themselves 2-0 down. The second goal was again crafted on the left flank, Eder leaving Michael Carrick on his heels and picking out Alan who shot first time past De Gea.
Ferguson, as he had against Cluj, deployed Wayne Rooney at the tip of a midfield diamond with Van Persie and Hernandez up front and it was the latter who gave United hope.
Serbian referee Milorad Mazic allowed play to continue after a foul on Van Persie and Kagawa took advantage to pick out the Mexican to head past a diving Beto after 25 minutes.
United pushed forward with intent after the break and drew level just past the hour when a corner was flicked on and Evans hooked in at the second attempt after initially mis-kicking.
Beto kept Braga on level terms wh
