Rajat Patidar and Faf Du Plessis revived RCB's innings with a 105-run stand for the second wicket after losing Virat Kohli on the first ball of he contest.
Dinesh Karthik hit 6, 6, 6,4 in the final over to propel RCB to 192/3.
Faf du Plessis carried his bat through for his unbeaten 73.
After losing both their openers in the first over, Rahul Tripathi and Aiden Markram put on a brief fight through a half-century stand.
Rahul Tripathi waged a lone battle for SRH in the chase, scoring yet another fifty.
Wanindu Hasaranga registered his career-best T20 figures of 5/18 to keep SRH to 125 in reply.