Having won the first leg in Madrid 3-1, Zinedine Zidane's side cruised into the last eight with a 2-1 victory at the Parc des Princes, where Ronaldo broke the deadlock.
His strike in the 51st minute saw the Portugal international join Ruud van Nistelrooy as the only players to score in nine consecutive Champions League matches, and laid the foundations for the holders to progress.
Edinson Cavani levelled on the night before Casemiro wrapped up a 5-2 aggregate win for Los Blancos with 10 minutes to play.
After seeing his side advance to the next round, Ronaldo took to social media to hail a big win for the two-time defending champions.
"A major victory in Paris," he posted on Twitter. "Come on team!"
Madrid will learn who their quarter-final opponents are on March 16 when the draw takes place in Nyon.