Cristiano Ronaldo dominated the pre-match headlines on his latest return to his former club, but it was Paulo Dybala who got the only goal of the game as a dominant Juve side made it three wins from three in the group.
Paul Pogba did hit the post in the final 15 minutes against his ex-employers, but that was a rare attacking highlight for the home side as they fall five points adrift of the Group H leaders.
Juventus took an early handle on the possession, but it was the home side that forced the first save from either goalkeeper when Wojciech Szczesny comfortably kept out a header from Pogba - appearing against his former club for the first time.
The visitors took the lead just one minute later, though, when Chris Smalling's sliding interception to prevent Juan Cuadrado from getting on the end of Ronaldo's cross only succeeded in diverting the ball into the path of Dybala.
The Argentine - who scored a hat-trick against Young Boys on matchday two - was left with a simple finish as he tucked the ball past David de Gea for his fifth goal of the season.
Juve came close again just five minutes later when Joao Cancelo exchanged passes with Ronaldo on his way into the box before drawing a save from De Gea with a low drive across the face of goal.
Massimiliano Allegri's side were controlling the game through their possession, and the frustration of the home fans began to grow as they watched their side make things far too easy for the visitors during the vast majority of the opening 45 minutes.
Rodrigo Bentancur was the next to threaten for Juve when he shrugged off his marker and met a corner on the half-hour mark but could not steer his header on target when he should have done better.
Juve continued to dominate proceedings and Ronaldo stung the palms of De Gea with a powerful free kick from range, before Blaise Matuidi drew another stop from the United keeper with his first follow-up, and then nodded a second off target after the ball had been lifted back into the middle.
Dybala curled another effort wide of the target before half time, and United will have been relatively relieved to go into the break with only a one-goal deficit considering the one-sided nature of the opening 45 minutes.
Jose Mourinho's side managed only three touches in the opposition area, one shot and 30% possession before the interval, leaving them hoping for a similar response to their recent second-half comebacks against Newcastle United and Chelsea.
Very little changed for the majority of the second half, though, and it took a world-class stop from De Gea to keep the score at 1-0 when he tipped Ronaldo's powerful first-time drive over the bar when it looked destined for the top corner.
United did show patches of improvement at times as the second half wore on, but genuine threats to the Juventus goal were lacking until 15 minutes from time when Pogba span away from his marker and saw his curling effort hit the foot of the post and bounce off Szczesny before going behind for a corner.
It proved to be the one moment of real attacking intent throughout the full 90 minutes from the home side, and even though Szczesny was forced into a late routine save to deny Anthony Martial, the hosts could have no complaints at coming away with nothing from a match which saw them outclassed for the most part.
The result means that Juve will guarantee top spot in Group H with victory in the reverse fixture against United next month and need just one more point to secure their place in the last 16, while United remain second and now two points clear of third-placed Valencia.
United have now won just one of their last seven matches across all competitions and one of their last six at Old Trafford, while they are winless in three successive home Champions League games for the first time this century.
Juventus, meanwhile, have now won 11 of their 12 matches this term to maintain their best-ever start to a season.
MAN UTD (4-2-3-1): De Gea; Young, Lindelof, Smalling,Shaw; Matic, Pogba; Rashford, Mata, Martial; Lukaku
JUVENTUS (4-3-3): Szczesny; Cancelo (Costa 87'), Bonucci, Chiellini, Sandro; Matuidi, Bentancur, Pjanic; Dybala (Bernardeschi 78'), Cuadrado (Barzagli 81'), Ronaldo