RCB chased down the target of 129 with four balls to spare with Sherfane Rutherford top-scoring with 28 while Shahbaz Ahmed made 27.
For KKR, Tim Southee took three wickets for 20 runs while Umesh Yadav got two.
Earlier, Royal Challengers Bangalore bowled Kolkata Knight Riders out for 128.
Andre Russell top-scored for KKR with a 25 off 18 balls.
For RCB, Wanindu Hasaranga took four wickets for 20 runs, while Akash Deep and Harshal Patel got three and two wickets respectively.
Brief Scores:
Kolkata Knight Riders: 128 all out in 18.5 overs (Andre Russell 25; Wanindu Hasaranga 4/20, Akash Deep 3/45, Harshal Patel 2/11).
Royal Challengers Bangalore: 132 for 7 in 19.2 overs (Sherfane Rutherford 28, Shahbaz Ahmed 27; Tim Southee 3/20, Umesh Yadav 2/16).
