The visitors could have been out of sight by half-time but goalkeeper Andrea Consigli made some good saves to keep them at bay as the forwards also spurned chances.
And they were made to pay for their sloppiness as Guglielmo Stendardo and Stefano Lucchini both scored in the second half to secure the win.
Giacomo Bonaventura had the first chance for Atalanta as he was found in the box by German Denis but his shot from 12 yards was saved by Daniele Padelli.
Marcelo Larrondo soon hit back with a rocket from outside the box and Consigli had to be alert to make a low save.
Luca Cigarini and Giuseppe Vives then traded long-range efforts before Padelli came to the rescue again, making a smart save after Denis had turned and got a shot away.
It was an end-to-end contest and the visitors should have taken the lead just after the half-hour as Omar El Kaddouri found himself alone in the area but Consigli was on hand to make another impressive save.
And just moments later they had another gilt-edged chance but Matteo Darmian could only hit the bar with a free header following a corner.
Torino were rampant and Consigli again had to be the hero as he made an outstretched save from Danilo D'Ambrosio's header to keep things level at the break.
D'Ambrosio teed up Larrondo just two minutes after the break but he could only drag his shot wide and moments later he was off target again as he skied a close-range shot over the bar.
Atalanta were to make the visitors pay for their profligacy in the 57th minute as Luca Cigarini's set-piece found Stendardo, who fired home after a goalmouth scramble.
Torino hit the bar again from an El Kaddouri free-kick and when the rebound fell to Ciro Immobile it looked easier for him to score.
But much like his team-mates he could not make the opportunity count as he blazed over the bar.
The hosts then doubled their lead with nine minutes to play with Cigarini again the provider, this time finding Lucchini who headed home at the far post.
There was still time for Denis to skim a post but the points were already secure.