The win lifted Mumbai City into second place in the league, four points behind leaders Hyderabad FC.
Kerala-based player Mohammed Irshad hit a 79th minute equaliser for NorthEast United.
Friday's Mumbai City vs Jamshedpur FC has been postponed.
David Williams came off the bench to score a consolation for ATKMB in the 60th minute.
FC Goa squandered the lead twice in the 2-2 draw.
Mumbai take on FC Goa, while Bagan clash with NorthEast United FC in the two-legged play-offs.
A win for Mumbai City FC in their final game against ATK Mohun Bagan would seal them a spot in next season's AFC Champions League group stage.
Goals from substitutes Boris Singh (72’) and David Grande (90') helped JFC inflict a second-straight defeat on the Islanders.
With this, Mumbai City remained on second spot with 34 points from 17 matches while Bengaluru FC jumped to sixth with 22 points from 18 matches.
Mumbai took the lead through Hugo Boumous (20th minute) and Adam Le Fondre (26th minute) but goals from Glan Martins (45th minute) and Igor Angulo (51st minute) made it all square for FC Goa.