The players were taken off the field twice before India resumed at the crease on 38-1 after in the seventh over, and then Ravi Bopara proceeded to tear through the order.
England's innings got off to a poor start, with Alastair Cook (2) edging Umesh Yadav to Ashwin, who took the catch.
Jonathan Trott made 20 before being brilliantly stumped by Dhoni to leave the Three Lions on 28-2.
The chase was at 46-4 by the time Joe Root (7) and Ian Bell (13) departed the crease, but Eoin Morgan accelerated the innings with the help of Bopara, who was putting in a great shift with the bat now.
The pair got England into a position from where they could win, but both men lost their wickets in quick succession to breathe new life into India's challenge.
The final over was given to Ashwin and it nearly started with Broad being stumped, but his foot was ruled to have been grounded following the third umpire's review.
Some effective death bowling left the hosts needing six off the final ball but Tredwell could not connect and the Indian fans were sent into raptures.