Pritam Kotal (12th) gave Bagan the lead but Thoi Singh (20th), Victorino Fernandes (22nd) wrested back the advantage to almost pull off an upset before Balwant (89th) headed in at the back post from a delectable Sony Norde cross.
The result saw Bagan, third in the standings, move to 22 points from 11 games, seven adrift of surprise leaders Aizawl FC who are 29 from 13 outings. East Bengal are second with 27 in their kitty from 13 matches.
Mumbai, at the opposite end of the spectrum, lifted themselves off the foot of the table with the stalemate, having 10 points from 13 games.
It took Mohun Bagan twelve minutes to take the lead. Norde's corner was flicked on by Yusa Katsumi to Pritam Kotal who had ghosted inside the box to volley into the roof of the net.
But their joy was short-lived when Mumbai scored twice in two minutes. While the first goal came out of nowhere, the second was due to a defensive error.
Pratesh Shirodkar's attempt was tapped in by an alert Thoi with the ball ballooning over Debjit Mazumdar and nestling into the back of the net.
Two minutes later, the Bagan defence was caught napping as Victorino sneaked in between Anas Edathodika and Eduardo Ferreira to turn in Clyde Fernandes' cross.
There was a surprise substitution for the away side as Clyde made way for Chinta Rao in what looked like a defensive shuffle.
At the half hour mark, Mumbai could have added insult to injury had Baljit converted Shirodkar's cross from close.
Bagan's woes were compounded when Debjit picked up a knock which was bad enough for him to not be able to continue.
He was replaced by Shilton Paul after play was stopped for sometime as he was being treated on the field.
There was drama after an hour of play when Kattimani illegally handled a back pass from seasoned campaigner Mehrajuddin Wadoo inside the box with the referee awarding the hosts an indirect free kick. There was no joy from it as Mumbai lived to fight another day.
Bagan had a gilt-edged chance to level things as Balwant found the post from a lofted Anas pass.
Jeje Lalpekhlua soon after had another good chance as he stayed onside but instead of pulling the trigger cushioned the ball for Balwant who could not get on the end of it.
Bagan's efforts paid off finally when Balwant nodded in Norde's sublime cross at the far post leaving Kattimani stranded.