Put in to bat, RCB powered their way to 49 for 1 in the first six overs and 89 for 1 after first 10 overs. But the next 10 yielded only 81 runs at the loss of six wickets.
A double strike in five balls by left-arm spinner Krunal Pandya (2/27) packed off the visiting team's danger men - captain Virat Kohli (33 in 30 balls) and AB de Villiers (29 in 21 balls). It also applied the brakes in scoring after the duo added 59 runs in 39 balls for the second wicket.
Debutant left-handed batsman Travis Head (37 off 24 balls) tried his best to up the run-rate and made 37 off 24 balls while adding 63 runs off 34 balls with Sarfaraz Khan, who made a quick 28 off 18 balls that helped RCB post a competitive score in the end.
Pandya was the pick of the MI bowlers with figures of 2 for 27 while Bumrah, who took two wickets in the last over. Tim Southee bowled economically without taking a wicket while Mitchell McClenaghan was punished in his latter spell to end up with an expensive 1 for 46.
Both Kohli (33 off 30 balls) and Rahul (23 off 14), who was hit on the helmet off the first ball he faced from left arm McClenaghan, were troubled by the movement extracted off the pitch in the first two overs.
The third over was dramatic as Rahul made room by drawing away to leg to swat the short ball from McClenaghan over covers for a six and then upper cut the next one for another maximum before turning the third off his hip for a four.