Buttler slammed an unbeaten 73 off 30 balls with the support of 5 fours and 6 sixes to help GT chase down the target of 170 losing only two wickets in 17.5 balls.
Sherfane Rutherford also made a significant contribution with his 18-ball 30 to catapult the run-chase.
Earlier, Sai Sudharsan slammed 49 off 36 balls to lead GT's charge right at the start.
Liam Livingstone's 54 and a couple of thirties from wicketkeeper-batter Jitesh Sharma and Tim David helped RCB to crawl to 169-8 in 20 overs on a ground which is known for high scores.