The Valencians unblocked the situation thanks to a clear goal from outside the box signed Gonçalo Guedes (43rd), after a free kick struck by hopeful Bryan Gil.
José Bordalas' men will therefore play in the 18th Copa del Rey final in the history of Valencia CF.
It will be April 23 at the Cartuja stadium in Seville.
Only downside: they may have lost their captain Gaya.
The defender, who wanted to play despite the risk of relapse of injury, had to give way to Toni Lato half an hour into the game (33rd), consoled by his teammates and applauded by the Mestalla stadium, but unable to continue.
At the end of the match, the Basque captain Iker Muniain had the opportunity to equalize (76th from a free kick, 78th), but the Georgian goalkeeper Giorgi Mamardashvili intervened and Marcelino's men had difficulty moving the Valencian block.
The Basques, finalists for the 2020 editions (final postponed to 2021 due to the pandemic and lost to Real Sociedad) and 2021 (lost 4-0 against FC Barcelona), will therefore not go to hang a third consecutive final.
In the final Valencia will find Betis or Rayo Vallecano, who face each other Thursday evening in Seville.
Nabil Fekir's teammates, who won the first leg 2-1 in the demanding Vallecas stadium, will do everything to try to grab the 5th final in club history.
The opportunity to go and try to glean their first title in the King's Cup since 2005 (2-1 against Osasuna) and the third in the history of Betis (1977, 2005).
© 2022 AFP