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.
The dismissal of striker Amauri left Parma toothless and unable to force the draw late on as Juve once again moved 14 points clear of second-placed Roma.
Napoli resisted a valiant fightback from doomed Catania to ride out a 4-2 victory at the Stadio Angelo Massimino.
First-half goals from Duvan Zapata (two), Jose Callejon and Henrique made the final outcome look like a foregone conclusion but bottom side Catania hit back through Fabian Monzon and Norbert Gyomber.
The pressure was lifted a little from AC Milan coach Clarence Seedorf as his side picked up their first win in five games by beating Fiorentina 2-0.
Philippe Mexes and Mario Balotelli scored the goals at the Stadio Artemio Franchi as the Rossoneri celebrated a rare victory to reignite fading hope of qualifying for Europe next season.
Elsewhere, Atalanta pushed Livorno even closer to the Serie A trapdoor while keeping alive their hopes of playing in Europe next season thanks to a 2-0 win in Bergamo.
Even without the suspended Maxi Moralez, Stefano Colantuono's men had enough firepower to see off the Tuscans with Giuseppe De Luca and German Denis netting the goals.
Genoa delivered a blow to Lazio's hopes of playing in Europe next season with a 2-0 win at the Stadio Luigi Ferraris.
Alberto Gilardino and Ioannis Fetfatzidis scored the goals for Gianpiero Gasperini's men, who can now look forward to another season in the top flight having put 39 points in the bank, only three less than the visitors.
Sassuolo are staring at the reality of a quick return to Serie B after 10-man Sampdoria moved into the top half of the table with a 2-1 victory at the Stadio Citta del Tricolore.
Samp always had the psychological edge after opening the scoring through Gianluca Sansone inside 18 seconds but Sassuolo are fighting for top-flight survival and levelled through Alessandro Longhi.
The chances were shared in a frenetic second half and it was Stefano Chuka Okaka who grabbed the goal that Samp needed to reach ninth place in the Serie A table, with Vasco Regini's red card at the death not affecting the outcome.
A solitary goal from Nene eased Cagliari's relegation fears and inflicted a fourth straight defeat on free-falling Hellas Verona.
The Sardinians had slipped dangerously close to the Serie A drop zone in recent weeks but a 1-0 victory at the Stadio Sant'Elia saw them pull eight points clear of 18th-placed Livorno.
In the other game, Chievo claimed a crucial three points in their battle to avoid relegation after swatting aside fellow Serie A strugglers Bologna 3-0 on Wednesday night.
Alberto Paloschi's brace and a last-minute effort by Luca Rigoni saw Chievo to an impressive win that vaults them out of the bottom three.
They are now one place and one point above Bologna, who occupy the last position of safety above the drop zone and hold a two-point advantage over third-bottom Livorno.