The hosts had put up a modest total on the board as they were all out for 131 with RCB leg-spinner Yuzvendra Chahal taking three wickets.
However, the hosts defended the total despite facing one of the biggest hitters in the game in the rival camp.
Australian paceman Nathan Coulter-Nile ripped apart the Bangalore top-order by dismissing skipper Virat Kohli (0), AB de Villiers (8) and Kedar Jadhav (9).