After seeing nearest rivals Inter Milan romp to victory against Genoa earlier in the day, the Bianconeri restored their six-point cushion at the top of the standings with a 3-1 triumph at the Allianz Stadium.
Juventus got off to the dream start as Dybala struck inside the opening minute, but Cagliari came back into proceedings and levelled superbly though Joao Pedro.
But the Sardinians were level for just 125 seconds as Filip Bradaric scored an own goal, with the midfielder perhaps fortunate not to give away a penalty shortly afterwards.
Cristiano Ronaldo rattled the woodwork at the end of a first half that was followed by a far-less interesting second period, with the Portuguese setting up Juan Cuadrado for a late third.
While it was not an entirely convincing display, it acted as a solid warm-up for Wednesday’s Champions League clash with Manchester United.
Allegri’s side will seal progress to the last-16 if they avoid defeat against a United side that were undone at Old Trafford by Dybala, who needed just 42 seconds to break the deadlock on Saturday night.
Cagliari’s ball down the left flank was picked off and the Argentina international was played in, smartly turning away from two defenders and striking low past goalkeeper Alessio Cragno despite the forward slipping.
It was an ideal start that Douglas Costa quickly tried to add to, but Juventus’ comfort began to wane along with their intensity.
Medhi Benatia was adjudged not to have handled before Wojciech Szczesny impressively thwarted Leonardo Pavoletti, with Cagliari’s purpose eventually rewarded in the 36th minute.
Pedro brought down the ball superbly in the box and continued to strike a low effort inside the near post – a wonderful goal that was soon undone as Costa’s cross from the left was inadvertently turned home by Bradaric.
Matters could have perhaps been even worse before half-time.
The video assistant referee advised official Maurizio Mariani to watch an incident when Bradaric appeared to handle in the box but – after several replays – he decided against a spot-kick.
Ronaldo rattled the post from an acute angle in stoppage time, with a thrilling first half making way for a tepid second.
With Juventus only holding a one-goal advantage, there was still hope for Cagliari and Allegri turned to a back three in the final stages to see things out.
The visitors were pushing for a leveller, only to be caught out by Juventus’ rapid attackers.
Cuadrado put Ronaldo through down the right, with the star man unselfishly feeding back into the path of the Colombian to sweep home.