The win saw Juve move on to 35 points and extend their lead at the top of the table to five, at least until second-placed Napoli, Inter Milan and Fiorentina (both 28) played on Sunday.
The champions were keen to get back to winning ways after suffering their second defeat in a month, to AC Milan, last weekend and to give them a boost ahead of their crucial Champions League tie at Shakhtar Donetsk on Wednesday.
"It wasn't easy tonight," he told Sky Italia. "The derby is always the derby and getting back to winning again is really good for morale. It's a great way to prepare for the game against Shakhtar."
But the tide began to turn when Torino's Kamil Glik was shown a straight red in the 36th minute for a reckless challenge on midfielder Emanuele Giaccherini.
"The game was over with the red card," Torino coach Giampiero Ventura told Sky Italia. Juve's assistant coach Angelo Alessio added: "Glik's red card was obvious. Giaccherini could have suffered a really nasty injury."
Andrea Pirlo missed the spot-kick, sending it high over Jean-Francois Gillet's bar.
Giovinco made it 2-0 in the 67th when he shrugged off Danilo D'Ambrosio and directed a neat, angled shot past Gillet.
"It's difficult in Serie A to play 10 man against 11," added Ventura. "Maybe we would have lost anyway, even without the sending off, but we would at least have continued to challenge Juventus."
It was Alessio's last domestic game in charge before coach Antonio Conte returns after being banned from matchday duties for his part in a match-fixing scandal at his former club Siena.
"Antonio will be here next time," Alessio told Sky Italia referring to next weekend's match against Palermo.
"We're all really happy. Torino were really well organised, they have a system of playing which is really difficult to
