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Warner's knock was studded with 4 fours and 4 sixes.
Kedar Jadhav hit 2 sixes in his 19-ball 25 before Ashok Dinda had his caught by Mithun Manhas at long-on.
Warner reached his fifty off 24 balls.
Delhi lost their second wicket when Ashok Dinda had Sehwag caught behind by Robin Uthappa.
Uthappa took his second catch in the next over to dismiss Chand off Rahul Sharma.
Uthappa took his third catch to dismiss Ben Rohrer off Abhishek Nayar.
Dinda gave Pune the first breakthrough when he had Delhi Daredevils captain Mahela Jayawardene caught in the covers by Luke Wright.
The breakthroughs for Pune came after captain Aaron Finch won the toss and chose to bowl.
Kane Richardson makes his IPL debut for Pune. Also left out is Ishwar Pandey.
For Delhi, Morne Morkel, Ben Rohrer and Unmukt Chand are back.
Delhi Daredevils: Mahela Jayawardene (Capt.), Virender Sehwag, David Warner, Unmukt Chand, Ben Rohrer, Kedar Jadhav, Irfan Pathan, Shahbaz Nadeem, Morne Morkel, Ashish Nehra, Umesh Yadav.
Pune Warriors: Aaron Finch (Capt.), Robin Uthappa, Yuvraj Singh, Steve Smith, Luke Wright, Abhishek Nayar, Mithun Manhas, Bhuvneshwar Kumar, Ashok Dinda, Rahul Sharma, Kane Richardson.