Adil Khan (32nd), Diego Carlos (59th) and Rohit Kumar (77th) scored the goals to help Pune City bounce back from their lose against Chennaiyin FC in the last match.
After today's win, Pune kept their hopes alive of reaching the knockout stage as they are firmly placed at the third spot with 19 points, one behind second-placed Chennaiyin FC and two adrift of Bengaluru FC.
It was Adil Khan, who drew the first blood for Pune when he jumped over all his markers and found the back of the net with a solid header after Marcelinho took a curling corner kick.
Rohit Kumar put the final nail on ATK's coffin with a stunning goal from the edge of the box after being fed by Sarthak Golui, who dribbled past Taylor.
Pune will now host Jamshedpur FC here on Wednesday, while ATK faces Chennaiyin at home on Thursday.