The Serbian forward struck five minutes either side of the interval to put the Bianconeri in control after Angel Di Maria marked his Juve debut with a maiden goal at the Allianz Stadium.
Massimiliano Allegri's side was not at its best in possession but made its chances count, with its attacking contingent laying down a marker to its rival.
A shaky start from the host provided Sassuolo with encouragement and called Mattia Perin, in for the injured Wojciech Szczesny, into action to deny Gregoire Defrel on two occasions.
Juventus soon found some rhythm and made the breakthrough when Di Maria met Alex Sandro's cross by bouncing a volleyed effort over the head of Andrea Consigli.
Five minutes before the break, Vlahovic bullied Gian Marco Ferrari to win the hosts a penalty and stepped-up to confidently smash home from the spot to open his account for the season.
Sassuolo was the architect of its own downfall following the restart, Kaan Ayhan giving the ball away to Di Maria who fed in Vlahovic to double his tally and continue in the vein that saw him star last term.
Juventus took its foot off the gas in the remainder of the half to ease out a win, with Filip Kostic introduced for the final half hour in a comfortable debut environment.