Gabriel Fernandes drew the first blood with a bullet of a shot over East Bengal goalkeeper Gurpreet Singh Sandhu's stretched hands as Mumbai FC showed total domination on home turf.
In a match that saw several rough tackles, Mumbai FC's Darren Caldeira was rushed to hospital with injuries.
Mumbai FC striker Yusuf Yakubu made it 2-0 in the fourth minute of injury time before East Bengal found a consolation goal through Chidi Edeh in the final minute of the match.
The win propelled Mumbai FC to 19 points from 12 matches as they climbed one step in the I-League ladder to number five position, pushing Prayag United SC down to sixth spot.
Despite the defeat, East Bengal stay at fourth place with 21 points.