Paul Pogba scored the only goal of the game in the second half at the Stadio Olimpico, extending Torino's 18-year wait for a Serie A victory over their rivals.
The winning goal came in controversial circumstances as Carlos Tevez, who appeared to be offside, headed against the crossbar from close range before Pogba nodded home the rebound.
But the visitors were generally good value for the victory and created more clear-cut opportunities than their opponents.
And Conte was particularly pleased with the way his side maintained their focus.
"It's not easy to win here and we're delighted that we've managed to do so," Conte said.
"We were more alert and precise than we have been in other games, shutting Torino out in spite of their ability on the counter.
"We produced a little less going forward. Credit to Torino, they're well organised and it's tough to find space in behind."
Conte also revealed that he made tactical changes throughout the match in order to counter specific threats from Torino.
He added: "I switched Pogba and (Arturo) Vidal. Vidal was closely marked by Omar El Kaddouri and Paul was able to use his physical attributes to better effect.
"I also went to a four-man defence after we scored because I didn't want to leave three on three at the back."
