Luca Toni put Hellas ahead in the 36th minute from the penalty spot but Ciro Immobile drew Torino level early in the second half.
Alessio Cerci then put the visitors in front in the 53rd minute before Omar El Kaddouri wrapped up the 3-1 win 29 minutes from time.
The result sees Toro leapfrog Hellas into seventh in the Serie A standings, with both teams level on 36 points and on course to retain their top-flight status.
Toro went into the game trying to bounce back from last weekend's surprise 2-1 defeat to Bologna - their first home loss since September 29 - and looking for a boost ahead of their upcoming clash with league leaders Juve.
They had the first chance midway through the opening period when Immobile fed Salvatore Masiello in the box and his goal-bound shot took a deflection off a Hellas defender to go behind for a corner.
It was Hellas who took the lead though after being awarded a penalty, the referee pointing to the spot after Juan Gomez Taleb was brought down in the area by Torino defender Cesare Bovo.
Toni made no mistake and struck his spot-kick into the right corner of the net and out of Torino goalkeeper Daniele Padelli's reach.
Toro almost equalised before the interval when Bovo's venomous effort from 30 yards was met by a fine save from Hellas goalkeeper Rafael.
Although they did not manage to level the scores on that occasion, that was a promising end to the first half for the visitors and they picked up where they left off after the break and got back on terms almost immediately.
Immobile got on the end of El Kaddouri's pass and broke into the area before slotting the ball into the net.
That was in the 49th minute and only four minutes later Torino were in front.
El Kaddouri again acted as provider when he set up Cerci just outside the box and the Italian forward's bullet strike beat Rafael.
Hellas failed to react and Toro punished them with a third goal after the hour mark, with El Kaddouri this time getting his name on the scoresheet with a 25-yard effort into the bottom corner to seal the win.