Trailing 2-1 after the first leg in Turin last week, Madrid went ahead on 23 minutes with Cristiano Ronaldo making no mistake from the penalty spot - to draw level again with Lionel Messi on a record 77 UCL goals - after James Rodriguez was brought down in the box by Giorgio Chiellini.
The goal put Los Merengues ahead on the way goals rule but Morata, who played in last season's final for Madrid - struck in the 57th minute - chesting down a knock down from Paul Pogba before firing past Iker Casillas - to edge the Bianconeri back in front.
Despite a late onslaught on Gianluigi Buffon's goal - with Gareth Bale in particular prominent - Madrid was unable to find another goal as Juventus prevented an El Clasico final. The reward a date with Barcelona in the Berlin final on 7 June (AEST) and a shot at a third European title and first since 1996.
The Madrid team bus was welcomed to the stadium by the kind of throng usually reserved for a victory parade ahead of the match.
Roared on by an equally fervent crowd inside the Bernabeu, Marcelo carved out the host's first opportunity. within a minute.
The full-back raced down the left before whipping in a cross for Gareth Bale, but the Welshman – in need of a strong showing after heavy criticism of his first-leg display – headed over.
Madrid continued to look the more likely to break the deadlock in the early stages and, after bringing the ball down well in the box, Karim Benzema, who was back in the team after seven matches out with a knee injury, fired high and wide.
Ronaldo saw a free-kick drift over off the arm of Arturo Vidal, although there were few appeals for handball, before the Chilean drew a diving save from Iker Casillas with Juve's first shot at goal.
A dipping Bale effort had Gianluigi Buffon sprawling after 20 minutes, but the goalkeeper was unable to keep out Ronaldo's spot-kick soon afterwards – diving right as the ball flew straight down the middle.
The penalty had been awarded for Chiellini's clumsy tackle on Rodriguez, and chances for Ronaldo and Benzema threatened to compound Juve's misery as Madrid ended the half in the ascendancy.
Rodriguez went down in the box again shortly before the break, but this time he was shown a yellow card for simulation having tumbled under the challenge of Vidal.
Claudio Marchisio sent an effort just wide of the left-hand post at the beginning of the second period, but Marcelo reminded Juve of the threat posed by the home side with a shot that veered just off target.
However, the visiting side re-established its aggregate advantage three minutes from the hour. And it was that man Morata who took centre stage.
Casillas punched clear from a cross, but Juve kept the ball alive and Morata eventually sent a shot bouncing over the head of the Spain goalkeeper and into the back of the net from Paul Pogba's nod down.
As had been the case when he opened the scoring in the first leg, Morata opted for a subdued fist pump celebration but his team-mates could not hide their delight.
Bale saw numerous chances to test Buffon come and go as Madrid sought the goal that would bring about extra-time, while Marchisio had a golden opportunity to put the match beyond doubt kept out by Casillas.
That missed chance mattered little at the final whistle, though, as Juventus, which survived late penalty appeals for a Patrice Evra challenge on substitute Javier Hernandez, celebrated and left the host in despair.
