Zidane's men rallied with chances for Marcos Llorente and Francisco Feuillasier but it took 41 minutes to test visiting 'keeper Pol Freixenet, who saved well from Mateo Kovacic.
According to Diario Gol, Germany's national team Coach is still considered to be the Plan B in case Zinedine Zidane were to leave.
Desperately in need of inspiration, Zidane threw on Bale, and the Welshman made an instant impact, perfectly picking out Mayoral with the outside of his weaker right foot, allowing the striker to head in.
The result, although it got the job done, does little to ease the growing pressure on boss Zidane.
Defender Sergio Ramos, who broke his nose in the Spanish league match against Atletico Madrid nearly 10 days ago, has been practicing with a protective mask but will not play Tuesday.
"He wants to play the rest of his life at Real Madrid".
Bale had a goal disallowed for offside not long after Madrid's second goal. He loves Madrid, the city, the life and the club.
Elsewhere, Malaga could only draw 1-1 with Numancia after losing the first leg 2-1, while Celta Vigo beat Eibar 1-0 to book their place in the next round.
Numancia had won the first leg 2-1. With Real Madrid, of course, they feel that all of world football's stars should be playing for Los Blancos.
Leganes advanced 3-1 on aggregate by defeating second-division club Valladolid 1-0.