Marcelo Bielsa's side earned a 1-0 victory on the night at the Iberostar Stadium thanks to Ivan Ramis's own goal.
Ander Herrera had an early chance of the visitors, but his shot was off target.
Michael Pereira could have got Mallorca back in the tie midway through the first half when his shot was snuffed out by the Bilbao defence.
Iker Muniain proved to be a thorn in the side of the home side throughout the match, but he was unable to make the breakthrough with two efforts in the second half.
The decisive goal came in unfortunate circumstances as Ramis put the ball through his own net with 13 minutes to play when Juan Calatayud air-kicked the defender's backpass.
Mallorca's misery was compounded in injury time when Chico was show a straight red card for his reckless tackle.
Bilbao will now face Mirandes for a place in the final.