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Opener Ruturaj Gaikwad blasted 65 off 51 balls as CSK chased down a target of 146, scoring 150 for 2 in 18.4 overs.
Opting to bat, Virat Kohli smashed a 43-ball 50, while AB de Villiers also chipped in with a 36-ball 39 as RCB posted 145 for six in their stipulated 20 overs.
Sam Curran (3/19) was the most successful bowler for CSK with three wickets, while Deepak Chahar (2/31) took two and Mitchell Santner (1/23) claimed one.