Touring captain Alastair Cook won the coin toss and elected to put the home side into bat first.
It proved to be a positive decision by Cook as India were all out for 226 with two balls remaining of their permitted 50 overs.
Suresh Raina was India's top scorer, making 83 runs before he caught by Bell. It could have been different for Raina, though, because he was dropped on five and 61.
England's reply got off to a good start when openers Cook and Bell reached the 11th over with a 50-run partnership.
Even when Cook was bowled by Ishant Sharma for 22, Bell was assisted by the likes of Kevin Pietersen (6) and Joe Root (31), before Eoin Morgan was at the crease unbeaten on 40 when the winning runs were struck with seven wickets to spare.
Despite the victory, England have lost the five-match series 3-2.