Former Manchester City and Inter Milan striker Balotelli has returned to Italy to play for his hometown club, but his debut had been delayed as he sat out a four-game suspension for previous club Marseille.
Juventus were without Portuguese forward Cristiano Ronaldo, rested with a slight thigh problem, but the champions recovered from going behind after less than four minutes to an Alfredo Donnarumma goal - his fourth in five games.
Juventus goalkeeper Wojciech Szczesny got two hands to Donnarumma's powerful strike, but could only push the ball into the net.
Brescia defender Jhon Chancellor let the champions off the hook five minutes before the break, diverting the ball into his own goal, with Bosnian midfielder Miralem Pjanic completing the comeback, volleying in on 63 minutes.