Madrid now carries an 18-match Champions League home unbeaten streak stretching back more than three years to a defeat against Schalke 04 on 10 March 2015.
The good news is the Old Lady still has a league title to worry about. In the other quarterfinal second leg of the day, Bayern Munich will play at home against Sevilla.
Yet that switch made little difference, and Blaise Matuidi made the most of a mistake from Keylor Navas to dramatically level the scores at 3-3.
Paulo Dybala's red card also leaves Juve shorn of one of their most potent attacking weapons for the return match at the Santiago Bernabeu on Wednesday.
Who else would decide the tie other than Cristiano Ronaldo - the man who had been the super-human difference maker in the first leg - who blasted the ball into the back of the net under huge pressure to take a last-gasp victory.
Real Madrid advanced to the quarterfinals after ousting Paris Saint-Germain in the Round of 16, while Juventus advanced to the quarterfinals after beating Tottenham in the Round of 16.