Rolando Bianchi had a a goal disallowed and then missed a header from close range, as Torino went close to gaining a two-goal advantage.
The home side controlled possession from then on and equalised 13 minutes from time when Amauri met a deep cross to score with an acrobatic volley.
Three minutes later the comeback was complete as Nicola Sansone smashed home from close range.
Amauri made the three points safe late on after driving forward and firing into the bottom corner under considerable pressure.
The former Juventus forward completed his hat-trick in stoppage time with a curling finish after fine work from Sansone on the left wing.