Braga face a 2-1 first-leg deficit against compatriots Benfica in their semi-final and, provided they can keep an clean sheet for the eighth time in nine games at home in Europe this season, one goal will be enough for a ticket to Dublin on May 18.
The eventual winners of the semi-final tie will almost certainly face Portuguese champions Porto, who take a 5-1 first-leg win to Spain's Villarreal for the other semi-final.
Since parachuting into the knockout stages from the Champions League, Braga have beaten Lech Poznan 2-1 on aggregate, Liverpool 1-0 and Dynamo Kiev on away goals.
Their distinctive stadium owes its nickname to the sheer wall of rock which forms one of the four sides to the ground and Braga have won six out of eight European games there so far this season.
Braga have only ever won one major trophy - the Portuguese Cup - but they finished as runners-up in the league last season and coach Domingos Paciencia says their rise has captured the imagination of the public, even if they are not the prettiest team to watch.
"People are happy about what Braga have been doing, there is great affection for this team," he told UEFA.com.
"Last season was very important. I felt, apart from the Braga fans, that a nation was supporting Braga... I felt Braga united many people.
"The image is that of a warrior-like team, a team that works, and that also helps the people to remember what football can actually be," added Paciencia.
"A team that works can have success that leaves me with pride in a certain way, for being the leader of this team and for feeling that these fans, in this city, are living through unique moments in their history.
"It makes me proud that I am the one that is leading this team."
Benfica have suffered a frustrating season domestically, finding themselves outclassed by Porto in the league and also losing out to their great finals in the cup semi-final.
Coach Jorge Jesus said that, even if the Eagles reach their first European final since 1990, it will not have rescued their season.
"It doesn't save the season. What I wanted was for Benfica to be champions again in the league."
Villarreal will be attempting to become only the fourth team to overturn a four-goal first leg deficit in European competition and the first since Real Madrid against Borussia Moenchengladbach in the 1985/86 UEFA Cup.
But Porto's record of seven wins in seven away games in the Europa League this season makes that a huge task.
Porto's Colombian striker Radamel Falcao has levelled Jurgen Klinsmann's record haul of 15 goals for the former UEFA Cup thanks to his four-goal performance in last week's first leg.
