The result means ATKMB could not break into the top-four, remaining fifth with 20 points from 12 games.
Mumbai's winless run stretched to seven games as the reigning champions remained sixth in the table with 19 points from 13 outings.
The brilliant Liston Colaco was hacked down on the left channel but despite green and maroon shirts' loud appeal, the referee did not give a free-kick.
Mourtada Fall then passed the ball to Ahmed Jahouh who dilly-dallied with Hugo Boumous pressing him hard.
Williams latched on to the loose ball, skipped past the keeper and put it past him.