Scorers: Juventus - Morata (8), Tevez (57pen); Real Madrid - Ronaldo (27)
Morata, who moved to Juventus in the summer shortly after helping Madrid to a record tenth European Cup title, didn’t celebrate after scoring the opening goal in the ninth minute.
Cristiano Ronaldo became the competition’s all-time top scorer with Madrid’s equaliser in the 27th minute but his former Manchester United team-mate Carlos Tevez also continued his fantastic season as he restored Juventus’ lead from the spot shortly before the hour after being brought down by Dani Carvajal.
Juventus, who last won the competition 19 years ago, will continue their bid to reach their first final since 2003 in the return leg in Madrid on 13 May.
Backed by a passionate home crowd, the newly-crowned Italian champions had the better of a frantic opening period.
The fans bayed for a penalty in the opening minute when Arturo Vidal fell between two Madrid players and Morata also went close.
The Spaniard did get his goal moments later. Claudio Marchisio slotted the ball through to Tevez and, although Madrid goalkeeper Iker Casillas got a hand to the Argentine’s shot, he only succeeded in deflecting the ball to Morata, who tapped in from close range.
That was Juve’s fourth shot on target in the opening nine minutes but it was to prove their last on goal of the first half as Madrid slowly got into the game.
Toni Kroos almost levelled immediately but Juventus goalkeeper Gianluigi Buffon dived smartly to his right to turn the shot around his post.
Ronaldo had been kept fairly quiet apart from an early free-kick which came off a Juventus defender in the wall. But he also went close to the equaliser when he sprung the offside trap to run onto a through-ball from Isco but could only send his effort wide of the right upright.
However, Ronaldo did level minutes later, heading into an empty net from close range after James Rodriguez hooked in a cross from the right of the area.
It was the Portugal star’s 76th goal in the competition – one more than Lionel Messi, whose Barcelona side host Bayern Munich in the other semi tonight.
Rodriguez almost got on the scoresheet himself four minutes from half-time but he headed Isco’s cross off the bar from five yards out and Marcelo volleyed the rebound narrowly over.
Juve had earlier had a chance to restore their lead but Marchisio’s long-range effort flashed just wide of the left upright.
The Italians were under pressure at the start of the second period and were camped inside their own half in the build-up to their second goal. A corner was cleared to Tevez, who went on a blistering run down almost the entire length of the field before being brought down by Carvajal.
The tension was palpable and the normally ice-cool Buffon couldn’t even bear to look, standing in his goal with his back to the action. However, Tevez blasted his spot-kick straight down the middle for his 29th goal of the season.
Madrid brought on Javier Hernandez, who had scored the late winner in his side’s 1-0 aggregate win over Atletico Madrid in the quarter-finals, and he almost leveled but just failed to get on the end of a cross from Sergio Ramos.
Juventus: Buffon, Evra, Lichtsteiner, Chiellini, Bonucci, Pirlo, Marchisio, Vidal, Sturaro (Barzagli 64), Morata (Llorente 78), Tevez (Pereyra 85). Subs Not Used: Storari, Pepe, Padoin, Matri.
Real Madrid: Casillas, Carvajal, Marcelo, Varane, Sergio Ramos, Pepe, Kroos, Isco (Hernandez 63), Rodriguez, Bale (Jese 86), Ronaldo. Subs Not Used: Navas, Fabio Coentrao, Lucas Silva, Arbeloa, Illarramendi.