Alan Silva scored twice inside the opening 20 minutes, before Javier Hernández halved the deficit before half-time when the United forward’s header crept into the net despite the best efforts of Braga goalkeeper Beto.
United centre-half Jonny Evans levelled the Group H encounter before Hernández completed the comeback with a superb header in the 75th minute.
It leaves Sir Alex Ferguson’s side five points clear of second-placed Cluj in Group H, and the Scotland midfielder is confident United can win in the return leg against Braga.
“After last year the aim was to get ourselves through the group as quickly as possible,” Fletcher told United’s website.
“One more victory should see us through and hopefully we can do it in the next game in Braga with two games to spare.”
Fletcher completed his third full match since returning from a lengthy lay-off with ulcerative colitis – and the 28-year-old vowed to make the most of his first-team opportunities.
“I feel fine. It was good to get another 90 mintues under my belt and the more of them I get the better I’ll feel,” he added.
“I’m fully aware there is huge competiton for places in midfield. I’ve just got to get as many minutes under my belt as I can and keep taking my opportunities when they come.
“There is great competition for places all over the pitch and the more of us that can stay fit the better it will be [for the team in the long run].”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news