Posting 192 runs for the loss of seven wickets, Hyderabad restricted MS Dhoni's side to 170 runs for the loss of six wickets in their 20 overs.
Faf du Plessis remained the top scorer for the side with his 33 while the rest of the batsmen failed to convert the start they got in the match.
Bhuvneshwar Kumar and Moises Henriques took two wickets as they restricted the CSK batsmen to 170.
With three sixes, Suresh Raina (23) tried to unsettle the bowlers but Henriques dismissed him to cut short his innings.
Earlier, riding on David Warner's 61, Hyderabad reached a competitive 192 runs.
Dwayne Bravo took three wickets for CSK.
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