Cristiano Ronaldo's 97th-minute penalty sent Real Madrid to the Champions League semi-finals in memorable fashion, going through 4-3 on aggregate against Juventus after a dramatic 3-1 loss on the night.
English referee Michael Oliver awarded Real a penalty with the tie seemingly heading for extra-time as Medhi Benatia knocked over Lucas Vazquez, with Juve goalkeeper Gianluigi Buffon sent off for protesting on his last Champions League appearance.
Ronaldo stepped up to beat Wojciech Szczesny, leaving Juventus devastated after a remarkable fightback to get to 3-3 after their 3-0 first-leg loss.
Real Madrid are the 6/4 favourites with Sky Bet to retain the Champions League title.
In a scintillating first half, Mario Mandzukic had scored with two far-post headers from right-wing crosses as Juventus looked to become the second Italian side in consecutive nights to overturn a three-goal deficit, following Roma's dramatic comeback against Barcelona.
Blaise Matuidi brought Juventus level in the tie after capitalising on Keylor Navas' error in the 61st minute, before the late drama at the Bernabeu.
Juventus, who could be backed at 66/1 with Sky Bet to reach the semi-finals before kick-off, came out desperate for the opener in a pulsating opening 45 minutes, and got the goal they craved after just two minutes as Mandzukic headed home at the far post from Sami Khedira's deft cross.
Navas blocked the ball at the feet of Gonzalo Higuain shortly after, before Gareth Bale's intuitive back-heel hit the side-netting at the other end.
Isco had a goal correctly disallowed for offside soon after as Real pushed for a killer fourth goal in the tie, with Buffon blocking well at his near post from Isco soon before Juventus' second.
It came through Mandzukic, who had replaced Juve's talismanic suspended forward Paulo Dybala for the second leg, with eight minutes of the half remaining, again nodding in at the far post as substitute Stephan Lichtsteiner found him from deep.
Real nearly made it 4-2 on aggregate before the break through Raphael Varane, but his header thundered off the bar, while after the interval Matuidi made the most of Navas' fumble from close range to bundle the ball over the line for an unprecedented leveller.
Juventus could be backed at 6/4 with Sky Bet to qualify after going 3-0 up at the Bernabeu and Real were odds-on favourites at 1/2 to progress at that stage.
Real missed several chances to take the lead in the tie through Isco, Varane and Ronaldo, before the late drama to cap off a quite unbelievable game of football.
Ronaldo leapt highest to head the ball down for Vazquez in the area, before the substitute was pushed in the back by Benatia. Referee Oliver waited, before pointing to the spot; cue pandemonium among Real players and anger from Juve in equal measure.
Buffon was shown a straight red for his protests, and they continued for another four minutes before Ronaldo struck into the top corner past Szczesny to win it for the hosts.
Post-match reaction
Cristiano Ronaldo insists referee Michael Oliver was right to award Real Madrid the injury-time penalty which he dispatched to send his side through to the Champions League semi-finals.
"I don't understand why they are protesting," he said in quotes published by Marca.
"Lucas was tackled from behind and if they don't give him the penalty, it's a goal.
"The pulse increased, but I calmed down, and I knew I'd be decisive."
Juventus chairman Andrea Agnelli called for VAR to be introduced to the Champions League after his side's exit from the tournament.
Agnelli felt the decision to award the penalty was wrong and claimed Oliver should not have sent Gianluigi Buffon off in what is expected to be his final Champions League game.
"VAR has to be introduced," Agnelli told Mediaset Premium.
"We will bring it forward and will look to make it happen.
"In this situation, it meant the possibility to move forward in the Champions League when we deserved extra time.
"We need to change the referee designator every two or three years. Buffon sent off? The referee didn't know how to handle the situation."