Jadeja, who is arguably the best fielder in world cricket, came up with a stunner to cut short Mushfiqur Rahim's stint.
The left-arm spinner trapped Shamim Hossain in front of the wicket to reach the milestone in his 182nd ODI.
Kohli was batting on 44 off 60 balls and had Ajinkya Rahane (20 batting) for the company during a stand of 71 for the fourth wicket as India ended the fourth day on 164 for 3 in pursuit of a world record chase of 444.
Dhoni, who had closed his eyes at the time of the final ball, lifted Jadeja to lead the celebrations as CSK scripted a famous win.
DC skipper David Warner and CSK all-rounder Ravindra Jadeja were in the thick of action.
Veterans Ajinkya Rahane and Ishant Sharma, who were previously in Grade B, have not been given contracts.
During the preview show, Chennai Super Kings' all-rounder Jadeja revealed that he initially wanted to be a pacer.
Anderson dropped to second place after England's stunning loss to New Zealand in the Wellington Test.
Jadeja has moved up to ninth position after his 10-wicket match haul in the second Test against Australia.
The Delhi Test loss would rankle Australia for they had a genuine chance of squaring the series.