Braga's task became even harder after just seven minutes when Mario Dorgeles - scorer of their first-leg winner - was sent off for a professional foul on Jan-Niklas Beste, leaving the visitors to play almost the entire match with a man down.
Freiburg made the advantage count quickly. Kubler opened the scoring in scrappy fashion when a clearance deflected off him and trickled into the net, before Johan Manzambi produced the standout moment of the night, curling a brilliant effort into the far corner to overturn the tie before half-time.
Braga twice came close to responding, hitting the woodwork late in the first half, but Freiburg's control grew after the break. Despite chances for Vincenzo Grifo and Matthias Ginter, it took until the 72nd minute for Kubler to seal the tie properly, heading in from a Grifo free-kick to put Freiburg firmly in command.
Pau Víctor's late header gave Braga brief hope, but Freiburg held firm to secure a historic victory - and the final whistle triggered extraordinary celebrations.
Supporters flooded the pitch at Europa-Park Stadion as players and staff embraced in scenes of pure relief and joy, with Freiburg sealing only the second major final in the club's history.
Kubler, who scored twice on the night, described the moment as overwhelming.
"It's a dream come true," he said. "The atmosphere was unbelievable throughout - the fans carried us. This is what you play football for."
Veteran defender Matthias Ginter, a World Cup winner in 2014, called it the biggest night the club has ever experienced - but stressed they now want to finish the job in Istanbul.
"This is the most important match in the club's history," Ginter said. "Now we have to go one step further. We're going to give it everything."
Midfielder Vincenzo Grifo also reflected on the emotional weight of the achievement, highlighting the bond between team and supporters.
"This club, this city, these fans deserve this," he said. "We won't sleep much tonight, but nights like this are special - you enjoy them."
Coach Julian Schuster was seen visibly emotional on the touchline and later joined in the celebrations as Freiburg's supporters celebrated a place in the final, where they will face Aston Villa.
The win also extended Freiburg's remarkable home record in the competition to 11 straight victories, matching a historic European benchmark, as belief continues to grow around a team now one game away from lifting a major continental trophy.
