Juventus, who sealed a record sixth consecutive Serie A title last season but lost the Champions League final to Real Madrid.
Juventus, who sealed a record sixth consecutive Serie A title last season but lost the Champions League final to Real Madrid, take a familiar spot at the top of the fledgling table.
Napoli also enjoyed a positive start with a comfortable 3-1 win at promoted Verona, where Arkadiusz Milik repaid Maurizio Sarri for a first start of the season with Napoli's second.
Referee Fabio Maresca made Serie A history at Juventus's newly-named Allianz Stadium by awarding a penalty following consultation with the VAR, but not even that could help an outplayed Cagliari as Juve keeper Gianluigi Buffon saved the spot-kick.
Juve coach Massimiliano Allegri, opting to play Dybala up front alongside Higuain with Mandzukic operating just behind, was quick to praise Buffon in what is scheduled to be the 39-year-old's final season.
"I expected the referee to give the penalty, luckily we have Buffon, the number one, in goal. He got us out of a sticky situation," Allegri told Premium Sport.
A week after a 3-2 SuperCup final defeat to Lazio that saw Dybala hit a brace, the Juve coach was mostly satisfied.
"The lads interpreted the game well, so I'm happy," added Allegri, who also had a special mention for hard-working Mandzukic.
"He's a big physical presence. When we're in difficulty, we rely on him. He can't do it all, but he's a big help."
A neat midfield move saw Mandzukic hold off his marker and half-volley Stephan Lichtsteiner's ball past Alessio Cragno on the half hour.
When Cagliari carved out their first real chance of the game, Juventus had Buffon to thank for stopping Diego Farias's curling drive from eight yards out.
Farias was gifted an immediate chance to make amends, but after Maresca took just over one minute to consult video footage following Alex Sandro's foul on Duje Cop, Buffon guessed right to save the Brazilian striker's effort on 39 minutes.
Dybala doubled Juve's lead in first-half injury-time, controlling Miralem Pjanic's brilliant quick ball over the top before firing past Cragno.
Juve spurned two chances in quick succession before Higuain made up for earlier misses from Dybala and Mandzukic by latching on to Alex Sandro's angled delivery to beat Cragno down low for his first goal of the season in the 66th minute.
Higuain received a standing ovation when he was replaced by midfielder Blaise Matuidi, the France international who signed from Paris Saint-Germain in midweek for 20 million euros ($23.5 million), before on-loan Bayern Munich winger Douglas Costa also made his Serie A debut.
Despite scoring once in a 2-0 Champions League qualifying win over Nice in midweek, Napoli boss Sarri left Dries Mertens on the bench to hand Milik his first start of the season.
After a bright opening period that saw Lorenzo Insigne miss a series of great chances, and Jose Callejon prove just as wasteful before the half-hour, it took a messy corner to give Napoli the lead when it came off the foot of Samuel Souprayen.
A crisp delivery from Insigne, following a great interception by Amadou Diawara, found Milik to strike past Verona 'keeper Nicolas first-time on 39 minutes.
Both Piotr Zielinski then captain Marek Hamsik missed clear chances before Algeria defender Faouzi Ghoulam put the match beyond reach on 62 minutes.
Napoli were reduced to ten men for the final minutes when Elseid Heysaj was shown a second yellow card for hauling down Daniel Bessa as he bore down on 'keeper Pepe Reina.
Giampaolo Pazzini stepped up to beat Reina down low with the penalty.