The draw takes Mumbai FC to 18 points from as many matches. While Dempo FC, who have played one match less than their opponent, have 17 points and need to win their next three games to avoid relegation.
Mumbai FC, who showed urgency in attack, had the first chance to score when Rahul Beke's lob from the right saw Josimar leaping high over his marker to head the ball, which was parried away by keeper Laxmikant Kattimani.
The tempo of the first half slowed down gradually. Holicharan Narzary, who created a couple of chances on the left, saw his left-footer hitting the bar and the rebound was cleared by a rival defender.
In the second half, both teams went all out with Mumbai FC finding the net in the 74th minute through Mohammed Rafi's diving header off a Jayesh Rane corner. However, referee A Rowan disallowed it after his assistant called it an off side.