India vs England: Suresh Raina, Rohit Sharma shine as India clinch ODI series
Raina was lucky to get a reprieve when he was caught by Cook in the slip but Davis signalled a dead ball as the bowler Finn had knocked the stumps over on his delivery stride, much to the relief of a near-capacity crowd.
Earlier, put into bat, England lost three wickets in quick succession in the middle of the innings after a reasonably good start, but the young Root unleashed a stunning counter attack to steer the total past the 250 mark, which looked doubtful at one stage.
Root, who clobbered eight boundaries and a six during his 45-ball blitzkrieg, and Pietersen were largely responsible for England's recovery.
Spinner Ravindra Jadeja was the pick of the Indian bowlers with 3/39 while Ishant Sharma 2/47 and R Ashwin 2/63 were the other wicket takers.
England's opening pair put on 37 runs for the first wicket before Ishant provided the breakthrough by evicting Bell, who perished to a rash stroke.
Bell decided to step out against Ishant but could not get to the pitch of the ball and Kumar pulled off a brilliant diving catch at the third man region.
Pietersen, who joined the action after Bell's dismissal, started off watchfully and took some time to get off the mark.
The experienced duo of Cook and Pietersen kept the scoreboard moving with gentle nudges and pushes and did not take too many risks as they steered England past 100.
The duo stitched 95 runs for the second wicket before off spinner Ashwin came to the hosts' rescue by dismissing Cook in what appeared to be a dubious decision by Sudhir Asnani.
Cook was wrapped on the pad while trying to play forward but the ball appeared to have pitched outside the leg stump line. Cook slammed 13 boundaries during his knock which came off 106 balls.