Supercopa de Espana champions after upstaging Barca in January, Athletic reached last season's Copa final but, due to the impact of the coronavirus pandemic, they are yet to play it – the match against their rivals Real Sociedad set for April 3.
Athletic are now gearing up for two finals in the space of 14 days next month, with a clash against Barca scheduled for April 17.
"These players have made Athletic Club history and sometimes that only happens once in a lifetime," Athletic head coach Marcelino said.
"They had to make the most of the moment and they did so."
Alex Berenguer's deflected, extra-time winner sealed Athletic's progress to back-to-back finals and saw them equal Real Madrid on 39 appearances in Copa del Rey deciders.
It completed a turnaround for the 23-time Copa winners, with Raul Garcia's penalty having canceled out Roger Marti's opener.
"We are going to take it step by step and enjoy today at least," Raul Garcia added.
"I am very happy because of all the work behind this and hopefully it will be a historic year.
"It's an honor to fight alongside this group of friends.
"We have a lot of confidence in each other, always help each other and that's what is giving us the results."
Athletic and Barca will play their ninth Copa final – the most-contested fixture in the competition's history.
In fact, Athletic will become in the first team to play two Copa del Rey deciders in the same month.