The Portugal international opened the scoring with a stunning free kick after just 16 minutes and then provided the assist for Mesut Ozil to seal the victory midway through the second half.
"It was a fantastic night for us," he told the club's official website.
"We played well and we scored two goals. It was a very important win for us.
"We expected a very hard game but we were better than them. It's always good to win the derby and that's what we have to take away from this."
Ronaldo’s strike took his tally to 20 goals in all competitions this season and he was happy with his night's work.
"On an individual level I am very happy with my performance because I scored a goal and provided an assist," he added.
"But the most important thing is the team, which played very well.”
The victory sees Los Blancos close the gap on second-placed Atleti to five points.