Braga were on the wrong end of an opening-day shock when they were humbled 2-0 by CFR Cluj at home a fortnight ago, but it was the Portuguese side who played the spoiler's role on Tuesday night.
After Ruben Micael stabbed in a 27th-minute opener, Braga soaked up the home pressure and, aided by some poor Gala finishing, sealed victory when skipper Alan netted a second in injury time.
Gala had lost just once in their previous nine home European fixtures but had seemingly settled after Custodio spurned an early chance by heading a Hugo Viana free-kick wide.
The hosts then took charge with Emre Colak forcing Braga goalkeeper Beto to save before Burak Yilmaz curled a 20-yard free-kick over.
It was the first of a number of misses for the Turkey international and he was off target again soon after, this time with a header, after he was picked out by Albert Riera's cross.
After failing to make their dominance pay in the opening half hour, the hosts were made to pay following a counter attack spearheaded by Braga's in-form summer signing Eder.
The 24-year-old bullocked his way into the area and after attracting a pair of defenders laid the ball back to Ruben Amorim. The midfielder's angled first-time strike was well kept out by Fernando Muslera but Ruben Micael was first to the loose ball to stab home.
Eder started to reveal the form that had seen him score three times in his past two games and he was only denied another when Muslera tipped around the post.
Gala's frustrations grew just before half-time as Yilmaz again headed wide of the target with a header.
Home boss Fatih Terim brought on Yilmaz's namesake, Aydin, at the break but he fared no better firing his first shot from 25 yards wide.
Burak Yilmaz finally started to find his range in the second period and he brought a save out of Beto, who had to move quickly to keep out a drilled effort from the edge of the area, before his header with 20 minutes left was comfortably caught.
Gala started to up the ante further in the closing stages but as they found their stride Beto proved unpassable.
The twice-capped Portugal international's best moment was to tip away a full-blooded Aydin Yilmaz 25-yard drive at full stretch.
As Gala became more frantic they left themselves exposed and Braga skipper Alan provided the killer blow in injury-time when he converted after an Eder assist.