Real Madrid C.F. were virtually assured of a place in the last eight after thrashing the Bundesliga side 6-1 in Gelsenkirchen in the first leg and coach Carlo Ancelotti rested a host of regulars for the return at the Bernabeu with an eye on Sunday's La Liga "Clasico" against Barcelona.
But the home side still had far too much quality for Schalke, particularly with World Player of the Year Ronaldo in electric form. The Portugal forward's double took his Champions League haul this season to 13, surpassing his previous best of 12 from the last campaign.
He has 41 in all competitions for Real Madrid C.F., the La Liga leaders, and is one short of the Champions League record of 14 set by Barcelona forward Lionel Messi in 2011-12.
Gareth Bale started on the bench but came on for the injured Jese in the eighth minute, and he set up Ronaldo for Real's 21st-minute opener. Schalke levelled 10 minutes later when a long-range Tim Hoogland effort deflected off Sergio Ramos and bounced past a stranded Iker Casillas.
Ronaldo, who also hit the crossbar and the post, scored his second of the night in the 74th and Alvaro Morata added a third for Real Madrid C.F. a minute later from another Bale assist.
It was Real Madrid C.F.'s biggest aggregate Champions League win after beating APOEL Nicosia 8-2 in 2011-12 and they go into Friday's draw for the last eight, when they could be pitted against La Liga rivals Barca or Atletico Madrid, in ominous shape.
"It's good for Spanish football to have three teams in the quarter-finals and shows it is in good health," Ancelotti told a news conference.
"We are coming into the 'Clasico' in good form and are very excited about the game. Generally speaking we are full of confidence and motivation."
They are unbeaten in 31 matches in all competitions since a La Liga defeat to Barca at the end of October and also meet their arch-rivals in next month's King's Cup final, raising the prospect of a rare treble.
The world's richest club are bidding to reach the Champions League semi-finals for a third consecutive season and are chasing the record-extending 10th European crown that has eluded them since they last won in 2002.
Schalke, who are third in the Bundesliga, at least avoided another drubbing and return to Germany to focus on securing a place in the Champions League next season.
"Anyone who watched the game tonight saw that we restored our honour today," Schalke coach Jens Keller told a news conference. "Two individual mistakes prevented us from getting a draw but I was pleased with the display nonetheless.
"Ronaldo didn't become the World Player of the Year for nothing. His qualities are outstanding."
Ronaldo has scored 32 times in his last 25 Champions League matches and has 63 goals in 99 appearances overall for Real and former club Manchester United.
Real can go seven points clear of third-placed Barca with a win on Sunday and Ancelotti used only four of the players who started the first leg at Schalke in his starting lineup.
Jese was deployed up front alongside Ronaldo and his Spain Under-21 team mate Morata, but was taken off on a stretcher after colliding with Schalke defender Sead Kolasinac.
Tests showed he had ruptured a cruciate ligament in his right knee and is likely to be out for several months.
"He has had bad luck and everyone at Real Madrid C.F. has had bad luck because we will lose a young player who has been doing very well this season," Ancelotti said.
After a goal for each side Schalke had some good moments late in the first half, delighting their 4,000-strong travelling support who drowned out the home fans inside the giant arena.
Former Real forward Klaas-Jan Huntelaar was played through in the 40th minute by teenage midfielder Max Meyer and his low shot scooted narrowly wide.
"We showed good character in the first half considering this tie was already decided," Schalke goalkeeper Ralf Faehrmann said on UEFA.com. "The goal that put them 2-1 up was unfortunate and then the game was over for us."