CSK rode on veteran Mike Hussey's 56 off 46 balls to chase down the modest 140-run target with just one ball to spare.
Opening the batting, Hussey, the Mr. Cricket who will be 40 in another five days, anchored the CSK innings with his vast experience and decorated his knock with three boundaries and two sixes.
Earlier, left-arm pacer Ashsih Nehra shone with the ball as CSK produced a fine bowling display to restrict RCB to a modest 139 for eight.
Nehra (3/28) picked up three crucial wickets to dismantle RCB's innings. He was ably supported by Ravichandran Ashwin (1/13), Mohit Sharma (1/22), Dwayne Bravo (1/21) and Suresh Raina (1/36).
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Chris Gayle top-scored for RCB with an unfamiliar 41 off 43 balls which was studded with two fours and three sixes.
Young Sarfaraz Khan (31 off 21 balls) played short little cameo towards the end to give RCB bowlers something to defend. Dinesh Karthik (28 off 26) also played a good hand but just when his team need him, the wicket-keeper batsman perished in search of quick runs.
But just when he was looking dangerous Smith departed in the first ball of the fourth over, caught by Mitchell Starc off Sreenath Aravind as the batsman went for a short-arm pull.
It could have been double blow for CSK in the next delivery had Gayle not dropped new man Faf du Plessis at the first slip.
After Du Plessis, it was time for Hussey to get a life as wicket-keeper Dinesh Karthik fumbled a sharp outside edge off David Wiese's bowling in the seventh over.