The Portuguese outfit played over an hour of the encounter with 10 men, but, after the game ended in a stalemate, they secured their place in the semi-finals on away goals after their 1-1 draw in the first leg.
Paulo Cesar's 29th-minute red card seemed to give all the impetus to Dynamo but a mixture of grit and determination from the hosts and a sorely lacklustre display from Yuri Syomin's side saw Braga progress.
Dynamo entirely failed to make the most of their numerical advantage, which was extinguished two minutes from time when Goran Popov earned a second yellow, and Braga would not have been flattered had they won the match outright.
As it stands, they will still make their first appearance in a European semi-final and join compatriots Porto and Benfica in the semi-finals.
Albert Meyong had the first chance of the match, heading over the from a decent position inside the penalty box in the third minute.
There were plenty of tough challenges early on too, with Popov twice guilty of mis-timing tackles inside six minutes.
Cesar was soon getting involved, taking down Oleg Gusev with a full-blooded lunge.
Artem Kravets had a hopeful punt at goal after 15 minutes before the referee issued his first card of the day to Andriy Yarmolenko.
Braga's Rodrigo Lima came to life soon after, shooting wide with his first attempt before working Dynamo keeper Olexandr Shovkovskiy from the edge of the area with his next effort.
Yarmolenko met Danilo Silva's cross after 25 minutes as the Ukrainians pressed but their task became easier five minutes later when Braga right-back Cesar was shown a straight red for an ugly scythe on Yarmolenko.
Braga held on stoically until the interval, working hard to stifle the opposition after a reshuffle at the back.
The Portuguese could even have gone ahead before half-time and were only denied when a quickfire double save from the alert Shovkovskiy frustrated Viana and Meyong.
Dynamo substitute Leandro Almeida started the second half in the same spirit as the first, with a foul on Lima within seconds of entering the fray.
Surprisingly it was again 10-man Braga who looked closer to breaking the deadlock, Lima collecting a fine through-ball before shrugging off his marker and firing hard at goal, where Shovkovskiy reacted quickly to palm over.
Dynamo remained in first gear as the clock ticked but with an hour gone they finally came close to breaking their duck, Roman Eremenko volleying left-footed from close range only for Artur to tip the ball wide.
Substitute Denys Garmash lifted Dynamo and was by some distance their best attacking outlet but he failed with a handful of attempts and it was Lima who looked most likely to give Braga a deserved goal when he blasted over from six yards.
The game finished on a sour note for Dynamo as Popov collected a second yellow for a foul on Alan.
Braga 0-0 Dynamo Kiev: Match Report - view commentary, squad, and statictics of the game as it happened.