The Turin giants stretched their lead at the top of the table to 14 points on Wednesday courtesy of a first-half brace from the Argentina striker, who is now the leading scorer in Serie A with 18 goals.
Tevez opened the scoring with a solo goal after 25 minutes and doubled their lead from close range seven minutes later at Juventus Stadium after Antonio Mirante had kept out Arturo Vidal's effort.
Cristian Molinaro gave Parma hope by pulling a goal back 62 minutes in, but Amauri was sent off for an elbow on Giorgio Chiellini and there was no way back as Juve continued their seemingly relentless march to another Scudetto and ensured the visitors remain in sixth spot.
Milan dealt a blow to fourth-placed Fiorentina's hopes of securing a UEFA Champions League spot as they secured a 2-0 win at Stadio Artemio Franchi.
Fiorentina went into Wednesday's clash on the back of an impressive 1-0 win at third-placed Napoli on Sunday, but they were brought crashing back down to earth by Clarence Seedorf's previously out-of-sorts side.
Philippe Mexes opened the scoring in the first half and Mario Balotelli struck after 64 minutes as Milan secured their first win six matches in all competitions.
Napoli put the disappointment of their defeat to Vincenzo Montella's side behind them by securing a 4-2 victory at bottom-of-the-table Catania.
Rafael Benitez's men stunned their beleaguered hosts by racing into a 4-0 half-time lead courtesy of Duvan Zapata's first two goals in Serie A and further strikes from Jose Callejon and Henrique, who opened his account for the Naples outfit.
Luciano Monzon and Norbert Gyomber pulled goals back after the break as Catania showed some fight, but defeat leaves them six points adrift of Bologna, who sit just above the relegation zone after they were beaten 3-0 at Chievo, with Alberto Paloschi scoring twice for the home side.
Second-bottom Sassuolo were unable to ease their relegation fears as they slumped to a 2-1 home defeat against Sampdoria, who had Vasco Regini sent off, while Livorno also remain in the bottom three following a 2-0 defeat at in-form Atalanta - who have now won their last five top-flight matches.
Cristian Ledesma was sent off as Lazio were beaten 2-0 at Genoa, while Nene scored the only goal as Cagliari got the better of Verona.
