Bale, the world’s most expensive player, had arguably his best game in a Real shirt to help make the second leg a formality.
The first came in the 13th minute when Bale cut in from the right and beat two players before laying the ball of to Cristiano Ronaldo.
Ronaldo’s backheeled return was intended for Bale but deflected off Felipe Santana into the path of Karim Benzema who fired home.
Bale doubled Real’s lead eight minutes later when he beat Felipe Santana with a body swerve and drove through a gap between two defenders before firing in off a post.
Ronaldo, Bale and Benzema were tormenting Schalke and Ronaldo made it three after collecting a sweeping pass from Bale in the 52nd minute.
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Ronaldo, made a fool out of defender Joel Matip with his customary stepovers before scoring with a fierce left-foot strike.
Ronaldo and Benzema played a one-two five minutes later with Benzema latching on to Ronaldo’s backheel before scoring Real’s fourth from an acute angle.
Bale got his second in the 69th minute with a cool finish. Sergio Ramos bisected the Schalke defence with a slide-rule pass and Bale beat the advancing Ralf Fahrmann with a crisp left-foot shot.
Bale was substituted 10 minutes from time but Ronaldo made it six in the last minute when he took Benzema’s pass, went around Fahrmann and slotted into an empty net.
There was still time for Klaas-Jan Huntelaar to volley in a stunning, if meaningless, consolation for Schalke.