Ruturaj Gaekwad (38) and Faf du Plessis (31) added 71 runs for the first wicket to set the tone for CSK's chase.
Earlier, RCB were off to a flying start with skipper Virat Kohli (53) and Devdutt Padikkal (70) laying a solid foundation with a stand of 111 runs for the opening wicket.
Kohli fell to the seasoned Dwayne Bravo after six boundaries and a six, while Padikkal hit five fours and three maximums before being dismissed by Shardul Thakur, as RCB stuttered after a fine start.
Suresh Raina (17) and skipper MS Dhoni (11) ensured that there was no twist in the tale, taking the side past the finish line.
The win took CSK to the top spot with 14 points. They overtook Delhi Capitals, who also have 14 points, but the yellow brigade has a better net run rate of 1.185 compared to 0.613 of the Delhi team.
Congress announcing 40% tickets to women in UP polls 'pure election drama': Mayawati
Mumbai Drug Bust LIVE: NDPS court to pronounce verdict on bail plea of Aryan Khan & others tomorrow
Scotland vs Papua New Guinea Live Score, T20 World Cup 2021: Berrington's 70 takes Scotland to 165/9
Eid-E-Milad-Un-Nabi 2021 Mubarak: Wishes, Quotes, Facebook statuses, WhatsApp greetings & HD images
Man gets women innerwear despite ordering football socks, Myntra's response leaves netizens angry
12 including 3 HDFC employees arrested for trying to withdraw money from NRI account
Google Pixel 6, Pixel 6 Pro launch: How to watch livestream, what to expect
Opinion | Why Hindu homes are being set on fire, temple vandalised again in Bangladesh?
SCO vs PNG Highlights T20 World Cup 2021: Scotland beat Papua New Guinea by 17 runs
Dhamaka trailer starring Kartik Aaryan, Mrunal Thakur will surely give you goosebumps. Watch video
Harbhajan Singh, Javagal Srinath awarded MCC life membership