Veteran Juve skipper and Italy international Buffon denied Diego Farias from 12 yards after on-field official Fabio Maresca used video technology to award Cagliari a first-half spot-kick following Alex Sandro's tackle from behind on Duje Cop.
It proved a costly miss for Massimo Rastelli's side, who were already trailing to the champions following Mario Mandzukic's opener in the 12th minute.
Paulo Dybala added to Cagliari's frustrations when he picked out the top corner on the stroke of half-time, with calls for handball in the build-up from the visitors ignored by the referee.
Argentina international Dybala was denied a second by the crossbar early in the second half, but compatriot Gonzalo Higuain got on the scoreboard as Juve bounced back from their Supercoppa Italiana defeat to Lazio in fine fashion.
Blaise Matuidi was handed a Juve debut from the bench after completing his €20million move from Paris Saint-Germain on Friday, getting 20 minutes to help see out a 38th successive Serie A home match without defeat for Massimiliano Allegri's men.
Miralem Pjanic curled an excellent free-kick narrowly wide, but Juve only had to wait until the 12th minute for the opening goal. Mandzukic guided a lovely right-footed volley from Stephan Lichtsteiner's right-wing cross beyond Alessio Cragno to put Juve ahead.
Paolo Farago fired over after Buffon saved a powerful shot from Farias before Cagliari had a fantastic chance to equalise when referee Maresca awarded them a penalty following a video review of Sandro's tackle on Cop.
Farias stuttered in his run-up and placed a poor spot-kick close enough to Buffon for him to save, and Juve punished the visitors further by adding to their tally before the break.
Pjanic sent an exquisite pass down the middle for Dybala, who was deemed to have controlled with his chest before beating Cragno with a fine finish into the top-right corner.
Within two minutes of the restart Dybala came agonisingly close to his second when, at the end of a flowing move, his cross-goal strike bounced down and out off the bar, with Mandzukic's follow-up header held by Cragno.
Farago volleyed a rare opportunity for Cagliari over the top of Buffon's goal, and Higuain showed him how to finish five minutes later.
At the end of a brilliant move involving substitute Sami Khedira and Sandro, Higuain placed a cross-goal shot through the legs of Marco Andreolli and into the bottom-right corner.
The Argentine was replaced by debutant Matuidi in the 70th minute, while Douglas Costa made his first Serie A appearance since joining from Bayern Munich by replacing Juan Cuadrado.
Dybala drilled narrowly wide at the end of a sweeping move in the 93rd minute, but Juve had already done enough to begin their bid for a seventh successive Scudetto with three points.
