Sixth-placed Parma arrived in Turin having avoided defeat in 17 games but quickly succumbed to a first-half brace from Tevez, who recovered his position as the championship's leading scorer.
Cristian Molinaro turned the game into a contest for its final 30 minutes yet the dismissal of striker Amauri left Parma toothless and unable to force the draw late on.
Juve are now once again 14 points clear of second-placed Roma and look set to clinch their third straight Scudetto in a matter of weeks.
Parma regularly flirted with the idea of competing with the champions-elect - Antonio Cassano and Molinaro went close in the early stages - but Juve and Tevez would own the night.
The Argentinian matched Ciro Immobile as the league's top scorer in the 25th minute when he brushed off the attentions of Gabriel Paletta to slot the ball past Antonio Mirante.
Only seven minutes later, he reclaimed the provisional Capocannoniere title.
His 18th goal came after he drove at the Parma box before feeding Arturo Vidal down the right.
The Chilean midfielder took a first-time shot and Tevez was there to sweep home the rebound.
The visitors were shell-shocked and could barely respond before the break - Cassano's left-wing cross to Molinaro came to nothing.
Parma took full advantage of the interval to regroup and refocus.
The warning signs were there for Juve as Paletta narrowly missed the mark with a header from a corner and, on 62 minutes, Molinaro halved the deficit with a powerful left-footed drive.
If one former Juve player had wounded his old team, another would soon provide his former employers with a timely fillip.
Parma were already up against it and lost a key player when Amauri saw red after elbowing Giorgio Chiellini in the 65th minute.
Juventus switched things up by throwing Fabio Quagliarella into the fray for Fernando Llorente and veteran striker made an instant impact by forcing a low save from Mirante.
All seemed lost for Parma as time ticked away but Roberto Donadoni's men were determined not to relinquish their unbeaten status without a fight.
Molinari gave former Gialloblu keeper Gianluigi Buffon a late scare from close range and Leonardo Bonucci was lucky to not concede a penalty at the death when grappling with Marco Parolo in the box.