Argentina international Dybala scored Juve's quickest Serie A goal in six years to put the hosts en route to a win that gives them 31 points after 11 top-flight matches – their best tally at this stage of a campaign.
Joao Pedro pulled Cagliari level in the 36th minute but an own goal from Filip Bradaric 125 seconds later gave the hosts an advantage they would not relinquish.
Cristiano Ronaldo was presented before the match with a commemorative shirt by Juve president Andrea Agnelli for scoring his 400th goal in Europe's top five leagues against Genoa last month, and the Portugal captain laid on a late third for substitute Juan Cuadrado.
Dybala got Juventus off to a brilliant start when he turned Fabio Pisacane and Luca Ceppitelli on the edge of the box and fired into the bottom-right corner despite losing his footing.
Cagliari were refused a penalty by referee Maurizio Mariani, who checked replays of Medhi Benatia heading the ball against his hand inside the box in the 18th minute, and only a brilliant Wojciech Szczesny save kept Leonardo Pavoletti out.
The Juve goalkeeper was unable to stop Joao Pedro firing inside the near post, but Cagliari were only level for two minutes. Bradaric inadvertently sent the ball into his own net when trying to intercept Douglas Costa's cutback.
Bradaric was fortunate not to concede a penalty for appearing to control the ball with his arm in the box, before Ronaldo thundered a shot from the left side of the area against the upright in stoppage time.
Massimiliano Allegri replaced Costa with Cuadrado for the second half and Juve found it tough to create more chances, but the Colombian finally added to their tally three minutes from time to stave off a potentially tense finale.
Juve rolling onto more history
The Bianconeri have already won seven straight Scudetti and you would have to be brave to consider any other team for the title in 2018-19 following their blistering start. Allegri's team have matched the record points total for this stage of a Serie A season and it is going to take something truly special to stop them marching on to Serie A glory once again.
