Kedar Jadhav top-scored with 69 runs off just 37 balls while captain Shane Watson contributed 24.
For Delhi, Chris Morris took three wickets for 21 runs while captain Zaheer Khan grabbed two for 31.
Brief Scores:
Royal Challengers Bangalore: 157 for 8 in 20 overs (Kedar Jadhav 69, Shane Watson 24; Zaheer Khan 2/31, Chris Morris 3/21).