SRH now have 12 points from 13 games and need to win their last league game against table-toppers Mumbai Indians to stay in the hunt.
RCB, who needed a win to seal their Play-offs berth, slumped to their third consecutive defeat in the tournament but stayed at second place in the table with 14 points from 13 games.
The 121-run target was always going to be a walk in the park for SRH in a small ground like Sharjah unless RCB inflicted early damage which they failed to do.
RCB removed SRH skipper David Warner (8) early but they needed more wickets upfront to be in the contest.
After Warner’s dismissal, Wriddhiman Saha and Manish Pandey (26 off 19) shared 50 runs for the second wicket in quick time to take control of the chase.
But some brilliant spin bowling from Yuzvendra Chahal in the middle overs and over cautious batting from SRH gave RCB outside hope.
Chahal dismissed Pandey and Saha and then Kane Williamson (8) was sent back by Isuru Udana to give RCB a ray of hope even though the contest was tilted very much in favour of SRH.
Jason Holder played a 10-ball 26-run cameo towards the end to take SRH home comfortably.
Earlier, SRH strangled RCB by picking up wickets at regular intervals after opting to bowl.
Young Devdutt Padikkal (5) and skipper Virat Kohli (7) departed in quick succession, falling to Sandeep Sharma (2/20). Sandeep has now dismissed Kohli for a record seven times in IPL.
AB de Villiers made a run-a-ball 24 before perishing and then Josh Philippe (32) again got a start but failed to capitalise. He was caught by Manish Pandey off Rashid Khan (1/24) in the next over as RCB slumped to 76 for four in 11.4 overs.
RCB were done in by some incisive bowling from SRH bowlers upfront, resulting in lack of partnerships, which is the vital for any team to post a decent total on the board.
RCB’s struggle with the bat can be gauged from the fact that they hit only nine boundaries and a six in their entire innings despite having the likes of Padikkal, Kohli, De Villers and Chris Morris up their ranks.
After the early blows, Washington Sundar (21) and Gurkeerat Singh (15 not out) tried to resurrect the innings with a 30-run fifth-wicket stand but they never got the momentum.
Towards the end, both Sundar and Morris departed in quick succession to add misery to RCB’s woes.
It was clinical performance from SRH bowlers as RCB batsmen struggled to get going after the early dismissals.
Jason Holder too shone bright with the ball with figures of 2 for 27 from his four overs.