United fought back with two headers from Javier Hernandez either side of a Jonny Evans goal that he scrambled in with his left foot after missing his kick with his right one.
United manager Alex Ferguson told ITV that conceding early goals was a fault they needed to correct.
“It has been the story of our season at home, starting badly and losing goals,” he said. “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.”
It was United’s third successive win and they top Group H with nine points, followed by CFR Cluj on four, after they drew 1-1 at Galatasaray. Braga have three and the Turkish side one.
In a lively match in Istanbul, Turkey, Cluj had Matias Aguirregaray sent off after 28 minutes and Felipe Melo missed a penalty for Galatasaray seven minutes later. Dany Nounkeu put through his own net to give Cluj the lead after 19 minutes, before Burak Yilmaz equalized for the home side 13 minutes from time.
Valencia ended BATE Borisov’s perfect start in Group F with Roberto Soldado’s hat-trick securing a 3-0 win in Belarus. With Bayern winning 1-0 at Lille with a Thomas Mueller penalty, Valencia, BATE and Bayern all have six points, with Lille on none.