Goals in the final five minutes from Arturo Vidal and Claudio Marchisio secured the victory at Turin's Stadio Olimpico, with home defender Kamil Glik sent off in between for a second bookable offence.
The result moved Juve 11 points clear at the summit with just 12 left to play for, but Conte insisted after the game that nobody was getting carried away just yet.
"We could have settled for what we had (at 0-0). Instead, we tried to win - as we always do," he said. "Now we just need one point and winning the Scudetto with three games remaining would be extraordinary.
"However, I'll continue to hammer away at the players until we've won the title, and they're fully aware of that."
Conte acknowledged relegation-threatened Torino had not made it easy for the defending champions.
"No stone was left unturned in our preparations for this game," the 43-year-old said. "Compliments to Torino - it wasn't easy to win, but we managed to score two incredibly important goals.
"We played a great game from a technical, tactical and behavioural point of view."