Angel Di Maria and Dusan Vlahovic Celebrate Goal
Juve went into the derby reeling from Champions League humiliation at the hands of Maccabi Haifa, but Vlahovic gave his coach some breathing room despite another poor team display against a Torino side who had no available strikers.
Serbia forward Vlahovic pushed in the winner with 15 minutes remaining to give Juve their first away win this season.
Juve are seventh, seven points behind league leaders Napoli, who host Bologna on Sunday evening.
However, the gap between Juve and the Serie A summit will increase again on Saturday if Atalanta beat Sassuolo in the day's late match and move a point ahead of Napoli.
Vlahovic's strike was his seventh of the season in all competitions for Juve and came seconds after Vanja Milinkovic-Savic had done brilliantly to keep out his header.
Milinkovic-Savic, the brother of Lazio midfielder Sergej, had also kept out Manuel Locatelli early in the second half with a finger-tip save.
Torino sit 11th on 11 points after collecting just one point from their last five fixtures, in which they have scored twice.
They are level with Empoli, who earlier ended Monza's three-match winning run with a 1-0 win which came thanks to Nicolas Haas.
It was the first loss for Monza coach Raffaele Palladino, who had won his first three matches as Monza coach after replacing Giovanni Stroppa last month.
Monza, who were repeatedly denied by Empoli's impressive goalkeeper Guglielmo Vicario, stay five points above the relegation zone in their first-ever season in Serie A.