The Islanders were up by two goals inside 15 minutes, as Fall headed home in the 9th minute before Singh converted from a brilliantly delivered Mandar Rao Desai cross six minutes later.
Despite trailing early in the game, Bengaluru struggled to come up with a response while Mumbai continued to dominate the game and saw more of the ball.
The game slowed down in the second half, and Bengaluru still could not come up with a plan to find goals and claw their way back into the game. They were given one when referee awarded a penalty after Cleiton Silva was adjudged to have been fouled by Fall inside the box. It was a contentious decision as replays showed Fall had made contact with ball first. Sunil Chhetri stepped up to take the kick, and converted it past Amrinder Singh.
However, Bengaluru's hopes of a comeback where soon put to bed when, in the 84th minute, Ogbeche, on as a substitute, headed towards the goal from a corner. Gurpreet Sandhu had initially collected the ball, but spilled it after he had gone to the ground, much to the frustration of the Blues.
Ahmed Jahou, already on a yellow card, was sent off in the 86th minute after referee booked him for the second time in the match.
Despite playing the remainder of the match with 10 men, Mumbai managed to hold on to their lead and collected all three points.