Athletic Bilbao beat Levante 2-1 - 3-2 on aggregate - to progress to the Copa del Rey final.
The Basque side will play Real Sociedad in last season's postponed Copa final on April 4 before taking on Barcelona in this year's a fortnight later.
Raul Garcia shot narrowly wide as Bilbao started strongly, but they fell behind against the run of play when Roger Marti fired Levante ahead after 17 minutes with a close-range finish.
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Garcia then equalised from the penalty spot on the half hour after being wrestled to the ground by Oscar Duarte when he appeared poised to tap in Inaki Williams's cross.
The Basque side looked the more likely side in the second half, but were unable to find the breakthrough in normal time before Berenguer's long-range effort deflected off Nikola Vukcevic and flew into the net eight minutes from the end of the extra period.
Bilbao coach Marcelino Garcia, who won the 2019 Copa while in charge of Valencia, could complete a unique hat-trick of back-to-back cup triumphs.
Barcelona secured their place in April's showpiece with an extra-time win on Wednesday.
The Catalans overturned Sevilla's 2-0 lead from the first leg to progress 3-2 on aggregate with goals from Ousmane Dembele, Gerard Pique and Martin Braithwaite.
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