Put into bat, the opening pair of Shane Watson and du Plessis gave CSK a good start by adding 30 runs in the first four overs.
After Watson's dismissal, Raina and du Plessis then anchored the innings, and played sensibly to further develop 120-run second wicket partnership help and help CSK post a fighting total as their lower middle-order failed to contribute.
Meanwhile, du Plessis also notched up his second half-century of the season off 37 balls.
Just when it seemed that the duo will comfortably steer Chennai to an imposing total, Raina mistimed a slower delivery by Curran to give an easy catch to Mohammed Shami at short fine-leg.
Sam Curran (3/35) starred for the hosts.
Curran struck again in the 19th over to send back a well-settled du Plessis, who fell short of his century by just four runs with Chennai's scorecard reading 163/3.
Shami then dismissed Kedar Jadhav (0) and Ambati Rayudu (1) cheaply in the final over as Chennai skipper M.S. Dhoni (10) and Dwayne Bravo (1) remained unbeaten at the end of 20 overs.