Outsiders Braga beat their more illustrious Portuguese compatriots on away goals after a 2-2 aggregate draw in the semi-final.
Braga will travel to Dublin for their debut European final on May 18 to face Porto, who swept past Villarreal 7-4 on aggregate thanks to their 5-1 triumph in last week's first leg.
Hosts Braga started sharply at their distinctive stadium, where a sheer wall of rock forms one of the four sides, and went ahead on 19 minutes when Custodio gave keeper Roberto no chance by towering above the defence to score after a corner.
"I am not the hero, we are a group of heroes. There are no words, there is an immense joy in the air here," Custodio said, as television images showed hundreds of Braga fans celebrating in the centre of the northern city.
Pressing hard, Braga gave Benfica scant room to deploy their flowing game, but the visitors came close to levelling the match when Argentine forward Javier Saviola sent a scuffed shot against the post five minutes before the break.
Benfica continued to struggle and their first chance in the second half came on the hour mark when substitute winger Franco Jara sent a dipping shot wide from the edge of the box.
They then missed two chances in the 79th minute when Nicolas Gaitan forced keeper Artur to touch away a fierce shot and Luisao sent a header wide from the ensuing corner with Saviola arriving seconds too late at the far post.
Braga responded with two chances of their own in the 84th minute, Custodio and Hugo Viana both forcing Robert into reflex saves with powerful drives as they held on to book a spot in the final.
"We deserve to be in the final, justice was done and this is very gratifying," Braga coach Domingos Paciencia said.
"The final is there for us to win, that is obvious. We have already shown we can do it," added the coach, who spent most of his playing career as a striker at Porto.
His side dropped down to the Europa League from the Champions League group stage and then knocked out Liverpool and Dynamo Kiev before meeting compatriots Benfica.
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