In a scrappy, turgid affair devoid of any pattern or fluency, Tevez's 16th Serie A goal of the season just before the hour mark was enough to separate the two sides at Stadio Angelo Massimino on Sunday.
Midway through a first half littered with fouls and scuffles on the field, both Antonio Conte and Rolando Moran were dismissed by referee Antonio Damato seemingly for disagreeing with a number of the official's decisions.
The breakthrough arrived in the 59th minute, when Pablo Daniel Osvaldo knocked down Andrea Pirlo's long pass into the stride of Tevez, who powered low into the bottom left-hand corner from just inside the area.
Catania, struggling desperately at the bottom of the table, had Gonzalo Bergessio sent off midway through the second half for a second bookable offence after leading with his arm in an aerial challenge with Giorgio Chiellini.
The red card seemed to demoralise the struggling home side, who up until that point had fought hard to combat their illustrious opponents.
The win, Juventus' sixth Serie A success in a row, leaves the Turin giants 14 points clear of Roma as they continued their seemingly inexorable charge to a third successive Scudetto.
Their beleaguered hosts, meanwhile, remain rooted to the foot of the table, four points adrift of safety.
The opening to the game saw three bookings inside the first 15 minutes, with Pirlo's off-target free-kick the closest either side came to a goal.
Alexis Rolin headed wide for the hosts from close range, then Damato sent both coaches from the touchline midway through the half.
Conte appeared incensed with a decision made by the official, who jogged over to the technical area and dismissed the Juve coach before also sending his opposite number Maran to the stands.
Osvaldo came close to opening the scoring 12 minutes after the break, sending an acrobatic effort narrowly over the crossbar, before providing the chance for his strike partner Tevez to break the deadlock two minutes later.
The Italy international nodded Pirlo's raking pass perfectly into Tevez's path, and the Argentina international burst forward before unleashing a shot that crept in at the far post despite a strong hand from Mariano Andujar.
The goalkeeper faired better 15 minutes from time, tipping behind another dangerous set-piece from Pirlo, before Tevez ought to have put the game beyond doubt six minutes from time.
After robbing Norbert Gyomber on the halfway line, he raced clear on goal but sent his effort wide of the post with only Andujar to beat.
It mattered not as Juve held on for the win to take a step closer to the title and simulataneously deepen Catania's relegation fears.
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