The win helped the struggling side to move to the seventh position in the eight-team league and with 15 points, they kept their hopes of making it to the semi-final alive.
Mumbai, playing their last home game, showed the intent to win right from their start and dominated the proceedings early on. Midfielder Lalrindika Ralte broke the deadlock in the 40th minute when his left-foot shot found the net after Tiago Ribeiro set it up perfectly for him.
The Sourav Ganguly co-owned side drew level 20 minutes later when substitute Baljit Sahni slotted it home. Taking a free-kick, skipper Luis Garcia made a short pass to Borja Fernandez, who set it for Sahni.
The Punjab player had come in just four minutes earlier in place of Rakesh Masih. The Peter Reid coached-side took the lead once again in the 76th minute when Manuel Friedrich headed the ball from a well executed free-kick from Ralte.
The hosts missed a golden opportunity in the 68th minute when Abhishek Yadav was caught napping inside the box and delayed taking a shot, allowing the defender to clear the ball to safety.
ATK too had a good chance in the 70th minute when Josemi took a terrific free-kick but Mumbai custodian Subrata Paul saved it as he came up with an acrobatic effort.
The final few minutes were anxious for both the sides as ATK found the net in the last minute of injury time but it was ruled as off-side. Desperately seeking a win to keep their hopes alive of making it to the semi-final, Mumbai played an attacking style of football and showed urgency in their passes right from the start.