Even a change in captaincy couldn't bring in luck for SRH as they went down by 55 runs.
This is the first time in Warner's IPL career that he has been dropped by any franchise for lack of form.
Under Warner, SRH have lost five of their six games as the Australian hasn't been in the best of form in the ongoing edition.
The win was CSK's fifth on trot which helped them leapfrog Royal Challengers Bangalore to the top of the table while Hyderabad stayed at the bottom.
The 30-year-old Natarajan had played only two games for SRH this IPL.
In the Super Over, SRH managed only seven off Axar Patel while DC scored the runs off the last delivery.
Natarajan had played only two out of the four games for SRH this season.
Khaleel Ahmed (3/21) and Abhishek Sharma (2/24) shone as Sunrisers bowled out Punjab Kings for 120.
Muralitharan, the leading wicket-taker in international cricket with 1,347 scalps, was admitted in Apollo Hospital, Chennai, for cardiac evaluation on Sunday.
Chasing a target of 151, SRH were bowled out for 137 in the final over.