A classy brace from Brazilian striker Rafael Bastos sealed victory in the first half with Mario Felgueiras in sparkling form between the sticks to keep his former employers at arm's length.
Braga controlled possession throughout at the Estadio AXA but finished the night bottom of Group H, while Cluj top the mini-league having scored one more goal than Manchester United, who beat Galatasaray 1-0.
A first half played at breakneck speed was born in the sixth minute as Custodio's goalbound effort was repelled at full stretch by Felguieras.
But Cluj survived the early pressure and went close themselves, Pantelis Kapetanos skewing a speculative drive wide, before the Romanians took the lead in the 19th minute.
Bastos raced onto Moudou Sougou's excellent pass following a quick break to beat the stranded Beto low to his right.
It fell to Felgueiras to stand tall and deny Antonio Eder a quick equaliser from six yards, the Braga striker soon trying his luck from outside the box before Hugo Viana saw his long-range drive smothered.
Their lead preserved, Cluj went on the offensive once more, Kapetanos carving open Braga's defence with a wonderful piece of skill before shanking wide of the target with only Beto to beat.
But their disappointment was shortlived as Bastos capitalised on a mistake by Nuno Coelho to weave between two Braga defenders and steer home a magnificent drive with the outside of his right boot.
Beleaguered Braga were presented with a chance to reduce the deficit before the break but Eder's weak effort was foiled by Felgueiras when it had been easier to score.
Felgueiras would spare his side's blushes once again after the interval, pulling off a stunning save as Ruben Micael roamed into his area to meet a dangerous cross.
Bastos might have completed his hat-trick in the 53rd minute when he slammed the ball over the crossbar before Viana unsuccessfully tried his luck from distance at the other end.
Marcio Mossoro embarked on a mazy dribble from deep but could not find the angle to beat Felgueiras as the hour mark passed.
Cluj retreated into their own half and were nearly punished as Ze Luis nodded just wide of a post after Coelho had stung Felgueiras' palms with a free-kick.
Kapetanos was presented with a clear chance to wrap up victory in the 76th minute but instead struck the ball fiercely against Beto's midriff.
Eder threw himself at Mossoro's accurate cross but could not keep his header down as Cluj held out for a first Champions League victory in four years.