Medium pacer Harshal Patel was the wrecker-in-chief for RCB, finishing with excellent figures of 5/27 to become the first bowler ever to record a five-for against Mumbai Indians in the lucrative league.
Opener Chris Lynn top-scored for five-time defending champions MI with a 35-ball 49 at the MA Chidambaram Stadium after Virat Kohli won the toss and opted to field.
Suryakumar Yadav contributed 31 off 23 balls while Ishan Kishan made 28 in only 19 deliveries.
Mohammed Siraj gave away just 22 runs in his quota of four overs.
Mumbai Indians: 159/9 in 20 overs (Chris Lynn 49, Suryakumar Yadav 31; Harshal Patel 5/27).
Royal Challengers Bangalore: 160/8 in 20 overs (AB de Villiers 48, Virat Kohli 33, Glenn Maxwell 39; Marco Jansen 2/28, Jasprit Bumrah 2/26).