Sunday's success leaves Marco Materazzi's side three points clear of second-placed Atletico de Kolkata, but crucially seven ahead of Pune City in fifth with just four regular-season games to go.
The free-scoring table toppers were made to wait for their opener at the Dr DY Patil Stadium, but Bruno Pelissari's 71st-minute effort gave them a platform to build upon.
Dhanachandra Singh and Cristian Hidalgo both netted in the final nine minutes to give the visitors a comfortable lead, and leave Mumbai, who were without Nicolas Anelka, slipping down the table and into sixth.
Atletico's impressive start to the season has begun to stutter and their 2-1 defeat to Kerala Blasters means they have only won once in their last four matches.
Goals from Iain Hume and Pedro Gusmao ensured David James' side kept their unbeaten home run intact, moving them up to third in the table.
Goa moved into the top four with a 2-0 triumph over Pune City, while Delhi Dynamos ended a six game winless run with their second victory of the campaign against NorthEast United.
Hans Mulder and Gustavo Marmentini struck in the first-half to give Delhi a 2-1 win, and lift them off the bottom of the table and back into contention for a top-four finish.
