Thoi Singh put the visitors in front at the stroke of halftime while Sean Rooney doubled the lead in the 60th minute to help Bengaluru restore their four-point lead at the top, while Mohun Bagan remained in danger of relegation with 24 points from 22 outings.
Mohun Bagan enjoyed a lot of possession in the opposition half but they never really tested Bengaluru custodian Pawan Kumar.
As the half progressed, both teams struggled physically due to the hot and humid conditions.
But Bengaluru broke the deadlock on the stroke of halftime almost out of nothing.
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A needless back-header by Denson Devadas sent Rooney behind the Mohun Bagan backline and the Australian's cross from the right flank was headed into the back of the net by Thoi.
Mohun Bagan were forced to replace Shilton at the interval due to injury with veteran Sandip Nandy coming on.
Bengaluru did not really get going in the second half but doubled their advantage at the hour mark as Rooney latched on to a mishit clearance from Sandip and found the back of the net with a well-placed shot.
Much like the first half Mohun Bagan never really looked like scoring and Bengaluru could have increased their lead when Thoi's cross found Robin unmarked inside the six-yard box but the India International put his header over the bar.