The AFC Cup semi-finalists went into the game six points adrift of the home side but moved into the striking distance of storming into the top three spots by claiming the spoils in a crucial match for the visitors.
James Saeed Moga gave East Bengal the lead with a 17th minute strike on a passing shot given by Raju Eknath Gaikwad before Edeh Chidi added another in the 78th as the visitors produced a dominant display over Bengaluru.
East Bengal played better football in first 15 and kept the pressure on the hosts, making several forays into their box.
The visitors could have scored more as they spilled their chances. Bengaluru goalkeeper Soram Poirei Anganba and his defenders had to be on their toes.
Also Read
Bengaluru, on the other hand, were predictable. They attacked only from the left flank, which the visitors anticipated and manned Bengaluru strikers to give away any chance for them to score.
The build-up for East Bengal's first goal came from Gaikwad in the centre, giving a passing shot to Moga, who dribbled the ball to his left and slotted the ball home to the dismay of 15,000-odd home supporters.
Most of play remained confined to Bengaluru's half in the first session and their goalkeeper had a busy day under the bar while his counterpart rarely collected the ball.