After salvaging a 1-1 draw in the first leg, Madrid neutralized Barcelona's passing game and counterattacked to perfection at the Camp Nou to hand its archrival its first home loss in any competition since last April.
"We played a great game," Ronaldo said. "We faced the game with a serious attitude, played better and scored three goals, which is tough to do."
It was also a second straight cup setback for the Catalan club, which is running away with the Spanish league but lost 2-0 at AC Milan in the first leg of its Champions League last-16 matchup.
While Messi had a quiet night, Ronaldo scored for a sixth straight visit to Camp Nou when he earned and converted a penalty in the 13th minute. Ronaldo hit again on the break in the 57th before Raphael Varane got his second goal of the series in the 68th to turn a convincing win into a rout.
Defender Jordi Alba scored late for Barcelona, but it was much too late to prevent Madrid from advancing 4-2 on aggregate. Madrid will play either Atletico Madrid or Sevilla in the Copa del Rey final on May 18.
After struggling in his first encounters with Barcelona, Ronaldo has become a nemesis for the Catalan club by scoring goals that have directly contributed to them losing titles the past three seasons.
Besides ending Barcelona's cup defense this campaign, Ronaldo scored here to dethrone Barcelona as league champions last season after also netting the winning header against Barcelona in the 2011 cup final.
"Ronaldo is our reference. He's vital for us," said Madrid captain Iker Casillas, who in a rare move spoke in place of coach Jose Mourinho, even though the goalkeeper sat out because of a broken hand. "He has shown how good he is not just today but in other 'clasico' matches. He is on a great run right now and we have to try and get the most out of it."
While Ronaldo put on one of his most memorable performances since joining Madrid, Messi couldn't keep up as the opposing defense again surrounded him and his teammates never picked up the slack.
A victory in the cup for Madrid would go some way toward salvaging what could be Jose Mourinho's last season with the club, after seeing its defense of the Spanish league title stutter and crumble.
With another "clasico" looming on Saturday at Madrid in the league, that title is firmly in Barcelona's grasp as it has a 12-point lead in the standings, with Mourinho's team another four points back.
That means Madrid can turn its attention to next Tuesday's Champions League match at Manchester United, following a 1-1 home draw in the first leg of their last-16 series.
Since being thrashed 5-0 in his first game in charge of Madrid in 2010, Mourinho has a record of four wins, six draws and six losses against Barcelona. And Madrid has come a long way with only one loss in their last seven contests.
For Barcelona, it was their worst defeat at the hands of its fierce rival since losing 4-1 in the Santiago Bernabeu in 2008.
The two cup losses also indicate that Barcelona is sorely missing coach Tito Vilanova, who is still undergoing treatment in New York after having a second tumor in two years removed from his throat in December.
Barcelona, which was again led by assistant coach Jordi Roura, has five wins, three draws and three losses since mid-January.
"This is a hard loss to accept but we have to pick ourselves up quickly," Barcelona midfielder Cesc Fabregas said. "We had our chances but they get out on the break so easily and we left too many spaces open. We need to learn from our mistakes (and) remember that we still have two titles to fight for."