Paulo Dybala struck in the 17th minute and the seven-time defending Serie A champions held on a night which saw Ronaldo back at his former home ground for the first time since 2013.
The win puts the Bianconeri in full control of Group H, with nine points from three matches and they were off and running early.
Just after the quarter-hour, after a swift Juve move down the right side, Dybala pounced from close range after Juan Cuadrado's sliding effort to get onto the end of a cross bounced in the Argentine's path.
His comfortable finish would provide the only scoring the visitors would need as they inch closer to securing their spot in the knockout stage.
The loss keeps United on four points from three matches, two points ahead of third-placed Valencia in the group. Young Boys remain in last place with one point.
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