Last season's beaten finalists held a 2-0 lead from the first leg and Cristiano Ronaldo, fresh from claiming the Ballon d'Or award earlier in the week, extended the advantage in the 21st minute.
Angel Di Maria then netted Real's second of the night 11 minutes after the break and, despite Fabio Coentrao's 85th-minute dismissal, Los Blancos sealed a 4-0 aggregate triumph.
Two goals in the final 10 minutes saw Espanyol survive a major scare to overcome Alcorcon 4-3 over two legs.
The Segunda Division outfit held a 1-0 lead from the first encounter and doubled that within four minutes as Oscar Plano found the back of the net.
Simao reduced the gap six minutes later and a Sergio Garcia penalty had the home side level, but when Javito put Alcorcon back ahead with 10 minutes to go, a major shock was on the cards.
But it was not to be as Victor Alvarez levelled things up in the 84th minute and just two minutes later Pizzi saved the home side's blushes.
Athletic Bilbao also had to overcome a 1-0 first-leg deficit as they beat fellow Primera Division side Real Betis 2-1 on aggregate.
Mikel Rico scored a goal in each half to ensure their progression.
In the night's other game, David Barral scored the only goal of the tie after 42 minutes as Levante beat Rayo Vallecano 1-0.