Having elected to field on winniing the toss, CSK restricted the visitors to 127/9 in their 20 overs.
CSK were boosted by an excellent display by the hitherto off-colour Ravindra Jadeja, who roared back to form with figures of 3/18.
CSK then overhauled the target with two overs to spare.
Opener Ambati Rayudu laid the foundation of a successful chase with 32 runs off 25 balls.
CSK skipper Mahendra Singh Dhoni gave the finishing touches with an unbeaten innings of 31 runs off 23 deliveries.
CSK: 128/4 in 18 overs (Ambati Rayudu 32, Mahendra Singh Dhoni 31 not out) vs RCB: 127/9 in 20 overs (Parthiv Patel 53; Ravindra Jadeja 3/18).