Cristiano Ronaldo netted a 23rd-minute penalty to give Real the upper hand before Morata stunned the Bernabeu when he rifled a shot into the roof of the net off goalkeeper Iker Casillas 12 minutes into the second half.
Spain forward Morata, a Real academy graduate considered surplus to requirements, also scored in the Italian champions’ 2-1 win in the first leg in Turin and Juve will bid for their third triumph in Europe’s elite club competition when they face Barcelona in Berlin on June 6.
Real pushed desperately for the goal that would have taken the game to extra time but squandered a host of chances and Juve remained on course for a treble of European and domestic league and Cup titles.
“Many people said Juve was not a team that deserved to be here and we have proved them wrong game after game,” Juve midfielder Arturo Vidal told reporters.
“They (Real) have some spectacular players but we are a very united team,” added the Chile international.
“We all know what Barcelona are, they have an incredible side, but we will see who is the best and we will put our lives on the line.”
After Ronaldo’s penalty following a clumsy Giorgio Chiellini foul on James Rodriguez, Real could have been further ahead at the break.
Ronaldo, Gareth Bale and Karim Benzema all wasted chances on a warm night in the Spanish capital with Real dominating as expected.
The match opened up in the second half and Juve were rewarded when forward Morata found space in the area after a clever layoff from Paul Pogba.
Chances came thick and fast at both ends and Rodriguez powered a shot narrowly over the crossbar, Real keeper Iker Casillas saved brilliantly from Claudio Marchisio and Bale nodded over when well placed.
“Juventus deserve to be in the final while we missed our chance,” Real defender Sergio Ramos told Spanish television.
“After the first goal it seemed like the tie was won but that wasn’t the case at all,” added the Spain international, whose side now face the prospect of ending the season without winning any of the Champions League or Spanish league and Cup.
Ronaldo, level with Barca forward Lionel Messi at the top of the 2014-15 scoring charts, became the first player to score at least 10 goals in four different Champions League campaigns.
He jointly holds the all-time goals record for the competition of 77 with Messi.
(Editing by Ed Osmond)