The prolific Portugal captain took his goal tally for the La Liga leaders to 41 for the season and 13 in the Champions League in 2013-14 as Carlo Ancelotti's side coasted to a 9-2 aggregate victory.
The tie was settled in the first leg in Gelsenkirchen a fortnight ago, when Ronaldo also scored twice as Real hammered the Bundesliga side 6-1 to put one foot in the last eight and Ancelotti's men finished off the job at the Bernabeu.
Ronaldo opened the scoring and restored Real's lead 16 minutes from time after Tim Hoogland finally opened his Schalke account and scored his first goal since January 2010 to equalise before the break.
Alvaro Morata sealed the victory a minute after Ronaldo's second goal and the former Manchester United forward struck the crossbar and the post in another outstanding display.
But there was concern for Real ahead of Sunday's El Clasico against Barcelona as Jese Rodriguez was forced off early on with a knee injury.
Ronaldo, Iker Casillas, Sergio Ramos and Xabi Alonso were the only Real players who started the first leg to keep their places in the side.
Kaan Ayhan made his first Champions League start as Schalke coach Jens Keller made three changes to the side hammered in the first encounter.
Gareth Bale was one of Real's key players to be given a rest, but the Wales forward came on just eight minutes in after Jese sustained a knee injury as a result of a Sead Kolasinac challenge.
Real were determined to finish the job in style and were in front after 21 minutes, when Bale picked out Ronaldo and the Portugal forward was left with a simple finish from six yards out.
Bale then produced a rapid turn of foot before setting up Morata, but the striker scuffed his right-foot finish with only Ralf Fahrmann to beat.
But Schalke were level against the run of play when defender Hoogland's strike from outside the penalty area deflected off Ramos and wrong-footed Casillas after 31 minutes.
Real responded and Fahrmann had to be alert to deny Isco and Morata. Former Real striker Klaas-Jan Huntelaar then spurned a great chance to give Schalke a half-time lead when his left-foot finish was just wide of the far post.
The prolific Ronaldo scented the opportunity to add to his incredible goal tally, but Fahrmann produced a fine save to keep out his downward header six minutes into the second half.
Schalke suffered a blow when Benedikt Howedes was withdrawn due to injury 11 minutes after the break and they were behind once again when Ronaldo drove forward 16 minutes from time and beat Fahrmann at his near post.
Ronaldo then spurned a chance to score a hat-trick when his shot struck the bar, but Bale set up Morata following up and the young striker made no mistake after he had been initially denied by Fahrmann. There was still time for Ronaldo to see a shot come back off the far post as he give Schalke a torrid time again.
