Having bowled India out for the first time in the series, England reached the 15-over mark in good order at 58 for one. Ian Bell was leading the way on 27 not out, with Kevin Pietersen alongside him.
Earlier Tim Bresnan claimed four for 45 in his final match before returning to England to a niggling elbow problem assessed.
India thought they had a breakthrough in the eighth over when Ishant Sharma appealed for caught behind against Cook. India were aghast when Sudhir Asnani said no, with television replays inconclusive. Bell hit his fourth and fifth boundaries in the ninth over, the latter an imperious off drive.
India paid for the lack of a second slip when Cook flashed Bhuvneshwar Kumar through the vacant position but the left-hander was gone soon after when Sharma bowled him with a sharp cutter.
Earlier, England made good use of morning conditions having asked India to bat first. Despite long-term concerns over Bresnan's elbow he proved he was still fit enough to cause India problems, sending Rohit Sharma and Virat Kohli back with successive balls in the fourth over.
Both men fell to full, swinging deliveries and both were held at second slip by James Tredwell, who showed off some impressive juggling skills after fumbling Kohli.
Yuvraj Singh survived the hat-trick ball but was soon gone for nought, squared up by Steven Finn and floating a catch to Eoin Morgan at point. Opener Gautam Gambhir managed 24 before he was caught by the diving Bell off Tredwell, making it 49 for four. Raina and Mahendra Singh Dhoni rebuilt before Finn returned to trap the home captain lbw for 15.
Ravindra Jadeja proved the perfect foil for Raina, accelerating the run-rate with two straight sixes and taking the score to 136 for five with 15 overs left. It was Tredwell who eventually ended the 78-run stand, Jadeja going on the attack but only managing to loop a catch to point.
Raina was now playing a lone hand and reached 83 before pulling the recalled Chris Woakes straight to Bell at mid-wicket. Ravichandran Ashwin (19) and Kumar (31) both had fun towards the end, which came when Bresnan took the last two wickets in the final over.