Cristiano Ronaldo scored a late penalty to help Los Blancos, who have won three of the past four editions, make their commanding 3-0 advantage from the first leg count and turn back a valiant comeback attempt from Juve.
However, the enthralling match was full of anxiety for the home side as Max Allegri's men nearly duplicated the feat performed by Serie A brothers Roma, who overturned a 4-1 first-leg loss to Barcelona on Tuesday night.
And the visitors stated their intent just seconds after the opening whistle, taking advantage of some slack Real defending to give their hopes of an improbable comeback early life.
In the second minute, Mario Mandzukic guided his header across Keylor Navas and into the gaping net after a curled Sami Khedira cross found him free from Dani Carvajal at the back post.
The teams took turns trading gilt-edged chances soon after, with Gonzalo Higuain failing to convert the best opportunity of all after a spilled cross fell into his path near the six-yard box.
Stephan Lichtsteiner was brought on for Mattia De Sciglio on 17 minutes after the former AC Milan right-back picked up an injury and couldn't continue.
As the game settled down, Real carved out the better of the chances -- Gianluigi Buffon's denial of Isco from point-blank range maintaining Juve's 1-0 goal lead on the day.
And it proved a vitally important save as Mandzukic cut Real's aggregate advantage to one with a second header on 37 minutes -- the Croatia forward out-leaping Carvajal and squeezing his header between Navas and the post after a Lichtsteiner cross from the right.
Zinedine Zidane brought off Gareth Bale and Casemiro after half-time but the moves couldn't stem the tide.
And Los Blancos surrendered a third just after the hour mark when Blaise Matuidi swept home at the goal line after Navas inexplicably dropped an in-swinging cross that fell into his chest.
But Real would get the goal they needed deep into second-half stoppage time after a retreating Medhi Benatia brought down Lucas Vazquez in the box after a Cristiano Ronaldo header found the second-half substitute with just Buffon to beat near the six-yard box.
The decision caused an immediate reaction from Juve players who saw Buffon sent off for dissent, leaving substitute Wojciech Szczęsny to stand in. But Ronaldo's shot from the spot was too good and Real booked their place in the semis.