Juventus looked to have staged a stunning revival to force extra time after Mario Mandzukic scored twice in the first half and Blaise Matuidi added a third on the hour mark after a goalkeeping clanger from Real's Keylor Navas.
The goals cancelled out Real's resounding 3-0 win in Turin a week earlier but Lucas Vazquez won an injury-time penalty and Juventus goalkeeper and captain Gianluigi Buffon was given a straight red card for venting his fury at English referee Michael Oliver.
Juve's substitute goalkeeper Wojciech Szczesny came on but Ronaldo blasted the ball beyond him to send Real into the semi-finals for a record-extending eighth season.
