The Portuguese netted from the spot either side of a magnificent Winston McKennie volley, as the Bianconeri leapfrogged their Spanish hosts into first place.
Whilst Blaugrana captain Lionel Messi was a threat throughout, he was unable to find a way past Gianluigi Buffon as Juventus were worthy winners.
Juventus carried the greater threat in the opening exchanges and Ronaldo was in the thick of the action. McKennie robbed the ball on the edge of the box and squared for the Portuguese, but his tame shot was easily stopped.
Yet with barely 10 minutes played Ronaldo was on the scoresheet, as he fired Juventus ahead from the spot. Collecting the ball and breaking into the box, the former Real Madrid forward was blocked by Ronald Araujo and contentiously, a penalty was awarded. Ronaldo stepped up and drilled down the middle to put the Bianconeri in the lead.
With only 20 minutes gone the Italians had doubled their lead in some style. Aaron Ramsey skipped through the Barcelona midfield and found McKennie, who kept the ball moving out to Cuadrado. A teasing flicked return pass into the box was acrobatically dispatched by McKennie on the volley, leaving Marc-Andre Ter Stegen with no chance.
Barcelona looked to hit back immediately and Messi was involved in proceedings for the first time, forcing Buffon to tip a driven effort from range round the post at full stretch.
Messi was becoming increasingly influential and tested Buffon once more after playing a one-two with Jordi Alba and firing low. The Argentine had a strong shout for a penalty on the stroke of halftime as he was brought down whilst shooting by McKennie, but after a lengthy VAR check his claim was waved away.
Despite Barcelona starting the second period well, they had soon conceded a second penalty. Whilst Ter Stegen pulled off a superb save to keep out Ramsey, a VAR check showed that Clement Lenglet handled in the build up. Stepping up again, Ronaldo drilled his spotkick into the bottom corner, sending the goalkeeper the wrong way.
The hosts almost found a way back in on the hour mark as Antoine Griezmann met a freekick from out wide, but his flicked header crashed off the frame of the goal.
Barcelona appeared to have won a penalty midway through the second half after neat passing on the edge of box allowed Messi to thread the ball to Griezmann, but whilst the Frenchman was brought down by Matthijs De Ligt, but was offside when the pass came to him.
At the other end, Juventus had a fourth goal chalked for offside themselves after Leonardo Bonucci bundled in from corner, but was offside as the ball came off Ronaldo into his path.
Despite Barcelona pushing for a goal to retain their position at the top of the group, an ineffective attack failed to get through and Juventus were well worth their victory.