The Argentinian also set up the fourth goal in a 4-0 win over Sassuolo as the Bianconeri put their midweek Champions League disappointment behind them.
Tevez earned a standing ovation after being withdrawn minutes after netting the fourth midway through the second half of a one-sided game.
Juve did not hide their disappointment in being eliminated from the Champions League in wintry conditions in Istanbul on Wednesday, but they channelled their frustration in the right way at the Juventus Stadium.
Sassuolo's resistance lasted only 15 minutes before Tevez scored his first.
The striker was on hand to knock the ball in from close range after Arturo Vidal's angled shot was fumbled out by Gianluca Pegolo.
Kwadwo Asamoah missed the chance to make it two when he dragged a shot wide of Pegolo's goal before Tevez teed up Peluso for Juve's second in the 28th minute.
The Argentinian's free-kick was met by the wing-back's strong header, leaving Pegolo no chance.
Tevez added his second and Juve's third on the stroke of half-time when he raced in to cut out a weak back pass before touching the ball past Pegolo and scoring into the unguarded goal.
The former Manchester City and Manchester United forward completed his first hat-trick in Italian football midway through the second half, providing the finish to an excellent team move which he started.
He passed to Vidal, who spread play for Mauricio Isla, and his low cross was met by Tevez in front of Pegolo's goal.
The 29-year-old was withdrawn straight after, earning a standing ovation before getting to take the ball home with him after his inspirational performance.