The goals came in a five-minute spell midway through the second half as Juve claimed the traditional Serie A curtain raiser for the third time in four years.
As Juve won both the Serie A and Coppa Italia titles last season, their opponents for this match were cup runners-up Lazio in what was a repeat of the 2013 Supercoppa.
Juve beat Lazio 4-0 in that match and they were again too good for their opponents on Saturday, although they had to wait until the 69th minute to get their noses in front at the Shanghai Stadium, with Mandzukic making the breakthrough.
The Croatia international, who joined from Atletico Madrid this summer, climbed between two defenders to glance home a header from Stefano Sturaro’s right-wing cross.
Dybala then wrapped up the win when he made it 2-0 in the 74th minute – less than quarter of an hour after coming on for Kingsley Coman.
Lazio failed to deal with Mandzukic’s ball into the area and Paul Pogba’s lay-back was smashed into the roof of the net by 21-year-old Dybala, who joined from Palermo in June.
Juve begin the defence of their Serie A title at home to Udinese next Sunday while Lazio host Bologna on Saturday.