Braga made a perfect start to their first UEL semi-final in 15 years, requiring less than 10 minutes to hit the front through Demir Ege Tiknaz.
Jordy Makengo failed to deal with a deep cross, and the full-back’s poor defensive header allowed Víctor Gomez to bring the ball down and roll it across for Tiknaz to slide it beyond Noah Atubolu.
The visitors looked dazed, but they were soon offered the chance to gain a foothold when a defensive mix-up on the halfway line opened the door for Jan-Niklas Beste to race in behind and into the box, where he played the ball across for Vincenzo Grifo to steer home his sixth European goal of the season.
However, rather than Grifo, it was Atubolu who made sure his team went into the break on level terms with a superb penalty save in first-half stoppage time.
The shot-stopper sprang to his right to thwart Rodrigo Zalazar after Philipp Lienhart was harshly penalised for holding Gustaf Lagerbielke following a VAR review.
An exciting end to the first period was soon followed by a cagey start to the second that eventually burst into life when Maximilian Eggestein forced Lukas Hornicek into an unconvincing stop, having latched onto a far-post knockdown.
As time ticked by, Julian Schuster’s charges appeared to change their ambitions from snatching a winner to protecting the draw as they dropped deeper in an effort to frustrate their hosts.
And their strategy nearly paid off until Dorgeles netted a dramatic winner in the second minute of stoppage time.
Atubolu could only parry Vitor Carvalho’s shot into the path of the 21-year-old, who stroked home the rebound to give his side a precious first-leg advantage ahead of the return fixture in Germany next week.
Flashscore Man of the Match: Noah Atubolu (Freiburg)