After losing the test series 4-0, India started brightly in the shortest version of the game and racked up 165 all out, only to see England reach their target with three balls to spare.
Eoin Morgan was the pick of the home team's batsmen, mixing powerful sixes with deft touches before he was brilliantly caught by Rohit Sharma for 49.
Kevin Pietersen also made 33 before being superbly stumped by captain Mahendra Singh Dhoni.
Despite the penultimate over by Munaf Patel yielding just three runs, Ravi Bopara (31 not out) and Samit Patel (25 not out) guided England home.
"You're always itching for a win," England captain Stuart Broad told Sky television.
"There are areas we can improve but I think we came back at India very well to restrict them after the start they got."
Earlier, opener Ajinkya Rahane hit 61 on his international debut and Rahul Dravid smashed three sixes in a row off spinner Patel to set India up for a sizeable total. Paceman Jade Dernbach took four for 22 for England.
World Cup 50-over winners India and Twenty20 world champions England now turn their attention to a five-match one-day series starting in Durham on Saturday.
