Beaten 3-1 by the same opponents last season, Juve fell behind after 19 seconds when Miralem Pjanic accidentally turned Goran Pandev's pass into his own net.
It got worse for Juve when Andrey Galabinov converted a penalty awarded with the help of a video review after the Bulgarian was tripped by Daniele Rugani. Juventus, however, claimed that Galabinov was offside at the time.
Dybala pulled one back in the 14th minute when he turned in Pjanic's pass, then equalised in first-half stoppage time, from another penalty, awarded after video technology spotted a handball by Darko Lazovic.
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Juan Cuadrado put Juventus ahead with a superb effort in the 62nd minute, the Colombian controlling Mario Mandzukic's chipped pass on his chest before turning inside his marker and curling a left-foot shot into the net.
Juventus were by now in control and Dybala wrapped it up in stoppage time when he cut inside a defender and sent a low shot between Mattia Perin and the near post to leave the Turin side on six points from their first two games.
Promoted Benevento were beaten 1-0 at home to Bologna in their first-ever home Serie A match and were denied a late equaliser when Fabio Lucioni's effort was ruled out for offside after a video review.
That game also saw referee Giampaolo Calvarese replaced by fourth official Daniele Chiffi for the final nine minutes after he appeared to suffer a calf injury.
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