The big news prior to kickoff was the exclusion of Lionel Messi from the first XI, but even after he was introduced in the second half, the five-time Ballon d'Or winner was unable to break the deadlock.
The forward received the ball in the centre of the box, and his attempt was easily caught by Marc-Andre ter Stegen, but the Brazilian showed promising movement and bursts of energy.
Cuadrado avoided an embarrassing moment when his header towards goalkeeper Gianluigi Buffon almost crept into the top corner, but other than that, Juve looked fairly untroubled until Ivan Rakitic unleashed a pin-point free kick.
The midfielder delivered the ball into the box with pace and it bounced before smashing off the post and towards Paulinho, who tried to head in the rebound but ended up missing the target.
A swift one-two between Cuadrado and Dybala almost ended in a goal for the former, but the ex-Chelsea man failed to control the ball with his first-time shot and the attempt flew over the crossbar.
Dybala was later involved again as he danced past three Barcelona players before turning and unleashing a thunderous hit from inside the box towards the far post, but over the bar it went.
Suarez tried to find the breakthrough after the half-time interval via a free kick, which he managed to lift towards the top left corner with the help of a slight deflection from the wall, but the ball dipped over the top.
Gonzalo Higuain had a rare opportunity to shoot when he collected the ball on the edge of the area before turning, only for his swinging shot to fall wide of the post.
Messi, who was brought on as a 56th-minute substitute, tried to make the difference from a free kick, which was delivered inches over the top of the bar with his left foot.
The Argentina international ramped up the energy for Barcelona and he played a hand in Lucas Digne's chance, which was wasted when he opted to square the pass rather than go for goal when he was one on one with the goalkeeper.
Juventus fans felt that their team should have had a penalty with 15 minutes left to play when Gerard Pique nudged Costa ever so slightly in a tussle for the ball, but the referee was having none of it.
There was a heart-in-mouths moment for Barcelona in injury time when Dybala's first-time hit forced a save from Ter Stegen, but in the end neither side could find the back of the net.
The result was good enough for Barcelona, though, who have made it into the knockout rounds as probable group winners, while Juventus still have a chance of qualifying as they sit second in Group D with a one-point advantage ahead of the final round of matches.
Massimiliano Allegri's men need to defeat Olympiacos in order to progress.