Tevez grabbed his first in the 15th minute, firing in the rebound after Arturo Vidal's effort had been saved by Gianluca Pegolo. The Argentina striker turned provider in the 28th with a free kick which Peluso headed in for his first league goal for Juventus.
Tevez doubled his tally on the stroke of halftime, pouncing on an error from Lino Marzorati before rounding the onrushing Pegolo and slotting into an empty net.
And Tevez, who scored a hat-trick for Manchester City earlier this year, completed his treble in the 69th minute, starting the move and finishing it when Mauricio Isla rolled the ball across for him to tap in from six yards.
Tevez was substituted moments later to a standing ovation.
Fiorentina moved into fourth place, two points ahead of Inter Milan.
Livorno remains a point off 17th-placed Sassuolo and safety, with Bologna a point further back.
- AP