Real took the lead in just the fourth minute, after Angel Di Maria cut inside from the right, played a nice reverse pass for Cristiano Ronaldo, who rounded Gianluigi Buffon in the Juventus goal to score.
However, they were pegged back in the 22nd minute, when Martin Caceres advanced down the right and swung over a fine cross to the far post. Paul Pogba headed from a tight angle, Iker Casillas managed to make the save but pushed it straight into the path of Fernando Llorente, who forced home the rebound.
Ronaldo put Real back in front from the penalty spot on 28 minutes. A free-kick came over from the left, and Sergio Ramos was pulled down by Giorgio Chiellini. Ronaldo fired the spot kick high into the top corner.
The result was put beyond much doubt after Chiellini was harshly sent off, putting his arm across Ronaldo who made rather a lot of the challenge.
Real now sit top of the group with nine points, having won all three of their games thus far, while Juventus have just two points from their three games.
4' - RONALDO GIVES REAL THE LEAD! What a start for Real! Angel di Maria cuts inside from the right, plays a nice reverse pass into the area for Ronaldo, who beats the offside trap, rounds Buffon and scuffs the ball a little bit, but it bounces over the line.
22 - LLORENTE LEVELS FOR JUVENTUS: Caceres dashes down the right and swings over a terrific cross to the far post. Pogba is unmarked, he does well to get a header in from a tight angle which Casillas saves, but the entire Real defence stands around and watches Llorente poke in the rebound. They deserved that.
27 - PENALTY TO REAL! A free-kick is swung over from the left, and Buffon claims, but not before Ramos is dragged over by Chiellini. Good decision.
28 - RONALDO PUTS REAL 2-1 UP! Despite several Juve players encroaching, Ronaldo puts it high to Buffon's right, right in the corner. Great penalty.
48 - RED CARD - CHIELLINI DISMISSED! Ronaldo knocked the ball past the Juve defender, who puts his arm across the Portuguese, who goes down hard, clutching his face. The referee makes the decision on advice from his assistant. Seems a little harsh.
Ronaldo now has seven goals in this season's Champions League, from just three games. The single-campaign record is 14.
Both teams had 13 shots on goal, with four on target for Real and five for Juventus.
Real had 56% of the ball, Juventus 44%.
TALKING POINT: Are Juventus in danger of not qualifying? Antonio Conte's side continued their disappointing start to the European campaign, and have now collected just two points from their opening two games, having surprisingly draw against both FC Copenhagen and Galatasaray. They now sit in third place after the Turkish side beat the Danes in Istanbul. They will probably have to win all three of their remaining games, including Real's return visit to Turin and a tough trip to Galatasaray in the final game.
REAL MADRID: Casillas 6, Arbeloa 6, Marcelo 6, Pepe 7, Ramos 6, Khedira 6, Illarramendi 7, Modric 7, Ronaldo 8, Di Maria 8, Benzema 5. SUBS: Bale 5, Morata 7, Isco 6.
JUVENTUS: Buffon 7, Caceres 7, Barzagli 6, Chiellini 4, Ogbonna 6, Vidal 7, Pirlo 7, Pogba 7, Marchisio 6, Tevez 6, Llorente 7. SUBS: Bonucci 6, Asamoah 6, Giovinco 7.
MAN OF THE MATCH: Angel Di Maria (Real Madrid): The Argentine winger seems to be the most vulnerable member of the Real side after the arrival of Gareth Bale, but if he plays like this again then he'll keep his place. A constant threat from the right, he produced an excellent reverse pass to set-up Ronaldo's first goal.
THE MATCH IN A TWEET