Ramos, who normally plays as a centre-back, was in the thick of the action throughout the quarter-final, second leg at the Bernabeu before Javier Hernandez struck two minutes from time to send holders Real through to the semi-finals for a fifth straight season.
Spain international Ramos helped Real dominate the midfield, an area in which they had struggled against Atletico in recent encounters, and it was their first win over their city rivals in eight meetings since last season's Champions League final.
Atletico barely had a sniff of goal, with Mario Mandzukic labouring ineffectively up front and fellow forward Antoine Griezmann forced into a more defensive role.
The dismissal of Atletico playmaker Arda Turan 14 minutes from time -- for a foul on Ramos -- dealt a huge blow to their chances of making the last four and Hernandez's late strike gave Real a deserved 1-0 aggregate win.
Ancelotti's ploy with Ramos was a surprise as he had used the same tactic in Real's La Liga 2-1 defeat at Barcelona last month and was widely criticised after the reverse.
"That's what the coach believed he should do and he (Ramos) played a fundamental role and we all benefited from his commitment," Casillas told reporters.
"Sometimes you also have to take on board your opponents' way of playing and today we were really firm and solid in the midfield," added the 33-year-old Spain goalkeeper.
"We didn't go backwards at any point, we defended really well and we had really clear chances in attack."
Real, chasing a record-extending 11th European crown, will find out their opponents in the Champions League last four when the draw is made on Friday.
La Liga rivals Barcelona, German champions Bayern Munich and Italian champions Juventus are also through.
"We're talking about four European champions, four top teams," Casillas said.
"Of the most recent semi-finals, they're the most even. They're going to be exciting, really special, and we're ready to play whoever we are drawn against."
Real are second in La Liga with six games left, two points behind Barca, and play at Celta Vigo on Sunday.
(Editing by Peter Rutherford)
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