The deadlock was broken after the away's side's lone attacker Eder powered his way way into the box and laid the ball back to Ruben Amorim. The midfielder's shot was parried into the stride of Micael, who anticipated the chance wonderfully well and gleefully converted before the Galatasaray defence were able to react.
Alan completed the victory on the break in the last minute of injury time.
Galatasaray had started much more assertively, keen to get three points on the board in the first home game of their European campaign after narrowly losing their opening group game to Manchester United two weeks ago.
Buark Yilmaz came closest to breaking the deadlock in the opening stages, flighting a 30-yard free kick over Beto’s crossbar after nine minutes and then heading over when well-placed two minutes later.
Micael's goal changed the game however, sapping the Turks of the confidence they had started with, converting well after excellent build-up play.
Good saves from home keeper Muslera prevented Braga from doubling their lead as the home side struggled to regain their composure following the shock of falling behind.
Eder was denied first, after 32 minutes, when the ball broke kindly for him in the six yard box and Muslera spread himself expertly to deflect the ball wide.
From the resulting corner a Paulo Vinicus header was also denied by the smart reaction of the keeper, amidst slightly panicked defending.
Just before the break, Yilmaz was presented with his easiest opening of the half, but mistimed a header that he watched flash wide of goal.
In the second half Yilmaz continued to be frustrated, missing further headers and close-range chances.
spectacular drive from 25 yards, the shot tipped onto the crossbar by the outstretched fingertips of Braga keeper Beto.
Yoham Elmander also came on for the Istanbul club but stuggled to make an impact as the Portuguese rearguard held firm.Braga's Alan scored at the death to secure the victory, and a crucial three points for the Portuguese side.