The hosts, thumped 7-0 in the same fixture last season, started strongly but in the end had little response to Atalanta's relentless attacks.
Simone Zaza fired against the bar in an early Torino attack and the Bulls went ahead in the 11th minute with the goal coming almost inevitably from their captain Andrea Belotti, who scored with an angled shot off Tomas Rincon's pass.
Atalanta were behind for just two minutes before captain Alejandro Gomez scored with a long-range shot.
Gomez also set up a second for Luis Muriel eight minutes later with a looping pass over the Torino defence and the Colombia international provided a spectacular finish with a low shot into the far corner of the net.
The goals continued to flow as Hans Hateboer scored a third for Atalanta from a Gomez cross in the 42nd minute before Belotti struck again to pull one back a minute later for Torino.
The second half began in the same vein with Torino's Alex Berenguer forcing a save from Marco Sportiello before Hateboer headed over from a good position at the other end.
Atalanta kept pouring forward and added a fourth in the 54th minute.
Muriel broke down the right and laid the ball into the path of Marten de Roon who sidefooted the ball into the corner of the goal to hand Torino their second straight defeat under new coach Marco Giampaolo following their 1-0 loss to Fiorentina.
Atalanta sat out the opening weekend as they finished their season later than most Serie A sides after reaching the Champions League quarterfinals.