The draw to decide the quarterfinal fixtures was held in Kuala Lumpur today (June 9).
Bengaluru will host the first leg of the quarter-finals at the Kanteerava Stadium on September 14 and travel to Singapore for the return leg on September 21.
Tampines Rovers had knocked Kolkata giants Mohun Bagan out of the tournament in the Round of 16 last month.
Bengaluru FC have exited from the tournament at the Round of 16 stage at the previous edition last year.
The Stags have taken part in the tournament seven times in the past and have featured in the last eight stage on three occasions from 2005 to 2007.