Mario Mandzukic's first-half brace stunned the Santiago Bernabeu before a terrible error from Keylor Navas saw Blaise Matuidi wipe out what remained of Madrid's commanding 3-0 first-leg advantage.
Mario Mandzukic's two first-half headers kept the dream alive before Blaise Matuidi capitalised on a Keylor Navas error to pull the Italians level with half an hour left.
Oliver pointed to the spot much and in the ensuing chaos, Buffon was sent off for his protests.
Former Arsenal 'keeper Wojciech Szczęsny came off the bench to face Ronaldo from the penalty spot, but unsurprisingly, the Madrid man produced the ideal penalty, firing high into the net to put his side into the last four of the competition.
It was always going to be a tough ask for Juventus to overturn a three goal deficit at the Santiago Bernabeu, and if they were to stand any chance of reviving their Champions League hopes then Allegri's side needed an early goal, and that's exactly what they got.
The second leg quarter-finals between Real Madrid and Juventus this night at Estadio Santiago Bernabéu may no longer be so referred to a clash of the titans if the past records of both sides are anything to go by.
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Juventus goalkeeper Gianluigi Buffon charged toward Oliver to protest the decision, and may have shoved him; video is shaky and other Juventus players swarmed around the official.
"I had to make changes, as I wasn't happy with the way we were playing".
Real Madrid's worst nightmare was taking place right before their eyes and their fans.
Juventus still won the match, 3-1, but Real Madrid will advance to the semifinal draw on Friday. Soccer can be cruel, and it's beyond cruel that the one thing missing from the Italian's resume is a Champions League winner's medal. Sami Khedira was played into space on the right and his clipped cross to the back post was headed home by Mandzukic.
Ronaldo failed to keep his header down four minutes from time when he escaped the attentions of Lichtsteiner to get on the end of Dani Carvajal's cross, but the Portuguese forward would have the final say.
The game looked to be heading for extra time before a chaotic final few minutes saw even the calmest of players lose control.