The Bergamo side's Italian league debut had been pushed back a week after it played in the UEFA Champions League last eight in Portugal last month.
But Gian Piero Gasperini's side proved it had lost none of its attacking style from last season with the most goals scored in Serie A including 7-0 against Torino last January in Turin.
"We are stronger than last year," Gasperini warned after Atalanta's third-place finish last campaign.
"You learn a lot from playing in Europe, and despite the difficulties we have suffered, we haven't given up.
"This year some valuable players have arrived and if we are lucky enough to recover (Josip) Ilicic we will be even stronger."
"It will be a season during which I will be able to rotate more players, last year I had a smaller squad available."
Andrea Belotti had put the hosts on the scoresheet first, connecting with a Tomas Rincon pass to rifle in after 11 minutes, the first of a double for the Torino captain.
But Atalanta hit back two minutes later with Argentinian Papu Gomez's rifling in from long range for his 100th career goal on his 200th Serie A appearance for Atalanta, leaving Salvatore Sirigu with no chance in the Torino goal.
Gomez then set up Luis Muriel for the second after 21 minutes, with Hans Hateboer grabbing a third after 42 minutes.
Belotti's header rekindled hopes going into the break but Atalanta dominated on returning, Muriel setting up Marten De Roon on 55 minutes to hand new Torino coach Marco Giampaolo his second defeat in as many games.
"It was the worst opponent we could have met,"Giampaolo said.
"They have been playing together for five years and have an extraordinary self awareness, it is difficult even for the most successful teams to face Atalanta, while we're trying to regain self-esteem."