A first-half rampage from the hosts was enough to give them a crucial win over their Portuguese visitors, who finished the game with 10 men despite an Alan strike
Both teams headed into this match knowing that a defeat could well spell the end of their hopes of progressing to the knockout stages and it was the home side that seized the early initiative.
From the opening whistle Paulo Sergio's men were dominant while their Portuguese visitors struggled to find any rhythm and on virtually their first real attempt on goal the hosts took the lead.
Brazilian Rafael Bastos was the orchestrator as he set up his Portuguese team-mate Rui Pedro to break the deadlock after just seven minutes.
After taking the lead Cluj did not rest on their laurels as they continued to push forward and it was that man Pedro who soon chipped in with his second of the night.
Bastos, a former Braga player, again played a key role in the lead up to the goal. Pedro somehow slalomed his way in between two defenders to steer the ball home and make it 2-0 after just a quarter of an hour of play.
But, to their credit, this time Jose Peseiro's side struck back almost immediately. Ruben Micael took control of the ball just outside the 18-yard box and delivered a fine through ball that teed up Alan from close range and the veteran Brazilian made no mistake as he pulled his side back into the contest.
The goal seemed to spark Peseiro's men into life as they very nearly made it all square moments later. Again it was Micael that was causing the problems for the hosts as he picked out Eder, who drifted in between two defenders, but unfortunately his tame effort was easily saved by Felgueiras.
Still trailing, Braga were very much the team in the ascendancy midway through the first-half as they seized control of the midfield and enjoyed the lion's share of possession.
Nevertheless, the Romanians continued to look dangerous whenever they had the ball and perhaps against the run of play it was they that would have the last say of the opening period.
Unsurprisingly it was Pedro who got himself on the scoresheet to seal his hat-trick. Modou Sougou did all the hard work with a penetrating run down the flank, before he cut the ball back for his team-mate to finish with aplomb and restore his side's two-goal advantage.
However, there was time for yet more drama before the referee called for the half-time break, when Douglao received his marching orders for raising his arm in the face of Camora, who certainly made the most of the contact.
The second-half was a much less eventful affair and it took almost 10 minutes for either side to register an attempt on goal.
Reduced to 10 men, Braga struggled to regain any sort of rhythm as the Romanians looked to extend their lead. Still, the teams did trade shots on goal, though it was not until the hour mark that a real chance was created.
Camora should have extended the host's lead and put an end to Braga's hopes of coming away with anything when he found himself clean through on goal.
But he took too much time and allowed the defence to get back in time to put him under pressure and eventually Beto had a relatively routine save to make.
As the game wore on, both sets of players appeared to tire as Cluj looked to close out the game. However, Braga did still manage to provide a scare with 15 minutes remaining on the clock when Mossoro had an effort ruled out for offside.
Cluj responded straight away and came within an inch of scoring their fourth of the night when Camora's shot rattled the post.
It was the Romanian side's second home win in eight Champions League matches but it could prove vital come the final round of group stage matches.
For Braga, their European campaign is in tatters and even a place in the Europa League seems unlikely after Galatasaray's surprise win over Manchester United.