The Portugal forward, runner up to Lionel Messi in Monday's World Player of the Year awards, netted twice inside the first 25 minutes at the Bernabeu as they sought to overturn a 2-1 first-leg deficit.
After Sergio Ramos was sent off with 17 minutes to go, Ronaldo eased the home crowd's nerves with his third and Sami Khedira wrapped up the scoring at the end.
A 5-2 aggregate win set up a meeting with Valencia next week.
Real Zaragoza were 2-0 winners at home to Levante to progress 3-0 on aggregate, and set up a last-eight meeting with Sevilla.
The 2010 Cup winners Sevilla were never seriously troubled having won 5-0 away at Real Mallorca in their first leg, and in a sparsely populated Sanchez Pizjuan progressed 6-2 on aggregate. (Reporting by Mark Elkington, editing by John Mehaffey)