Three first-half goals shocked the home side, who were constantly at risk from counter-attacks and set-pieces, unable to defend with confidence.
Sergio Ramos scored twice, the first coming from a simple Luka Modric corner, with no Bayern player marking him. A few minutes later, he and Real had their second when Pepe glanced on Angel Di Maria’s cross, and the Spain defender was lurking to fire past Manuel Neuer again.
Cristiano Ronaldo then scored his 15th of his Champions League campaign – a record – by sweeping home a shot at the near post after a textbook counter.
In the second half, Real were content to sit back and absorb any pressure, as Bayern had to score at least five goals to progress.