Antonio Conte's men are all but ensured of a third consecutive Scudetto and restored their 14-point lead at the summit by seeing off a spirited effort from Parma, who had previously gone 17 league games without defeat.
Tevez proved to be the key for Juventus, the 30-year-old taking his tally for the season to 18 with a brace that re-establishes his position as the top scorer in Serie A.
The Argentine striker gave Juve the lead with a fine individual effort midway through the first half, and then doubled the advantage in the 32nd minute with a typical poacher's goal.
Parma fought back and cut the deficit as Cristian Molinaro found the net against his former club to give the visitors' hope, which was effectively ended almost immediately after when ex-Juve striker Amauri was sent off for elbowing Giorgio Chiellini.
Defeat keeps Parma sixth in Serie A, behind Inter who can extend their advantage to three points with a win against Udinese on Thursday.
Key duo Paul Pogba and Fernando Llorente returned to the Juventus starting XI after being left out of the 1-0 win at Catania, but the hosts struggled to break down Parma in the opening stages.
And it was Roberto Donadoni's side who crafted the game's first real chance after 17 minutes when Cristian Molinaro connected with Alessandro Lucarelli's right-wing cross, only to be denied by a fine reaction save from Gianluigi Buffon.
However, the game was brought to life just eight minutes later as Tevez opened the scoring, powering past a pair of Parma defenders before slotting the ball home with a precise near-post finish.
That strike moved the former Manchester City man level with Ciro Immobile at the top of the Serie A goalscoring charts, but Tevez soon leapfrogged the Torino forward with his second just after the half-hour mark.
Tevez showcased quick reactions to fire home a rebound after Antonio Mirante had saved from Arturo Vidal's close-range effort.
Juve looked to be coasting towards victory and were made to pay for taking their foot off the gas in the second half as Parma drew level in spectacular fashion.
And it was former Juve wing-back Molinaro that pulled Parma back into the game after 62 minutes, finding the net with a fierce volley from the edge of the area that left Buffon with no chance.
Parma's hopes of a fightback were dealt a huge blow three minutes as Amauri saw red on his return to Turin for his ill-advised foul on Chiellini.
The numerical disadvantage seemed to galvanise Parma, who were denied a late leveller as Buffon pulled off a fine stop from Molinaro to prevent his old club from taking a share of the spoils.
