Madrid won the first leg 3-0 in Turin last week, when Ronaldo scored with a spectacular bicycle kick for his second goal of the match.
But Madrid managed to deny the rallying visitors after Lucas Vazquez was fouled by Medhi Benatia - Cristiano Ronaldo stepping up to convert the stoppage-time goal.
Ronaldo showed great composure to fire the ball past substitute Wojciech Szczesny - who had replaced Gianluigi Buffon after he was sent off for protesting the decision - to secure a 4-3 aggregate victory.
"I don't understand the protest by Juventus", Ronaldo told reporters after the game.
Madrid have been drawn to face Bayern Munich in the semi-final, with the first leg taking place at the Allianz Arena on April 25.
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Except the last few punches that she received, Mary Kom remained on top throughout to get the yellow metal. I hope they (Indian players) don't ever want to experience this any more", he said.
Real coach Zinedine Zidane made two early changes in bringing on wingers Lucas Vazquez and Marco Asensio for Casemiro and Gareth Bale at the start of the second half and said he gave his players a firm message.
The Italian veteran, who is set to leave Juventus at the end of the season, was given a standing ovation from the home fans as he walked off the pitch in what is likely to be his last act in a long and eventful career in the Champions League. Mario Mandzukic scored the first after just two minutes, heading home Sami Khedira's deft lofted pass, and the Croatian doubled Juventus's advantage on 38 minutes, this time powering home Stephan Lichtsteiner's cross with his head. Juve beat us and made things very hard for us with their tactics but our willingness to keep trying to get back in the game eventually gave us our goal. We were not good, and we have to admit that.
"Life goes on. I'm happy and proud of how we played, we made the impossible possible". He then changed his appraisal of the penalty to "more than controversial" a couple of hours later.
"The pulse increased, but I calmed down, and I knew I'd be decisive", he said. Despite this, the 33-year-old got his opportunity to make the difference right at the end, after calmly slotting in the match-winning penalty in the 97th minute.
The Serie A giants had fought their way back from a 3-0 deficit to pull level, but with extra-time looming Cristiano Ronaldo managed to clinch a insane win via the penalty spot.