The title holders took the lead through youngster Udanta Singh in the 26th minute, before extending their lead in the 68th minute, with Udanta finding the back of the net for a second time.
Sena Ralte finished things off for Bengaluru with an 89th minute strike, as Lajong failed to come up with a response against their formidable opponents.
In the day's first match, East Bengal salvaged a point against Aizawl FC with a last gasp equaliser from substitute Ivan Bukenya.
After going into the half-time break trailing by a goal owing to Gurwinder Singh's own goal, East Bengal were lucky to not concede again after Aizawl hit the crossbar early on in the second half.
However, Bukenya's 89th minute strike helped salvage a draw for the Red-and-Golds, as they managed to avoid defeat in the season's opening game.