Duckworth-Lewis target of 218 in 43 overs with seven balls to spare and now have an unassailable 2-0 lead with two games in play in the five-match series.
James Anderson (4th L) is congratulated after dismissing Parthiv Patel during the third one-day international cricket match at the Oval cricket ground in London.
While Alastair Cook's team can move about India into fourth place in the one-day world rankings by winning the last two matches at Lord's and Cardiff, MS Dhoni's side would simply settle for leaving the country with at least one victory to their name.
The injury-hit Indians were defeated 4-0 in the Test series, lost the lone Twenty20 international and have been beaten in two of three 50-over matches, with the other rained off.
It took just four balls for James Anderson to give England the perfect start after Cook put the world champions in as Ajinkya Rahane edged to Jonathan Trott at first slip.
India needed Rahul Dravid to steady the ship but the 38-year-old's aging legs let him down as he was brilliantly run out by Anderson in the sixth over after rashly attempting a quick single.
Anderson soon added Parthiv Patel to his list of scalps and India's struggles continued when Virat Kohli became the fourth man to go, caught behind off Anderson with the score on 25.
Suresh Raina fell when he mistimed a wild slog off Broad, edging to wicketkeeper Kieswetter to put India deep in trouble at 58-5.
But, to the relief of the massed ranks of Indian supporters, Dhoni made his 39th one-day 50 in 69 balls and, aided by some overly defensive field settings from Cook, he was able to rebuild India's innings.
Ravindra Jadeja and Dhoni put on 112 before the skipper skied a mistimed drive to Cook off Tim Bresnan.
Despite that blow, a 59-run partnership between Jadeja, who finished with 79 from 89 balls, and Ravichandran Ashwin ensured India made a respectable score.
But England openers Cook and Kieswetter, who hit three big sixes, took the hosts past 50 without loss by the ninth over.
Munaf Patel broke the partnership when he trapped Cook lbw for 23 with the score on 60.
Kieswetter brought up his 50 in 41 balls, yet he perished moments later as Jadeja found some spin to knock out his middle stump.
India's spinners suddenly posed a serious threat and England were reduced to 89-3 after Ashwin bowled Trott.
The hosts added six more runs before rain stopped play for an hour, leaving England with a new Duckworth-Lewis target of 218.
Ian Bell didn't help England's cause when he was run out for 23 by Dhoni after he started for a single and turned back too late.
Youngster Ben Stokes showed his lack of experience as he bowled round his legs by Ashwin and were England wobbling at 138-5.
Fortunately for England, Bresnan and Bopara -- staking his claim for a permanent place in the team with 40 in 41 balls -- turned the tide with a crucial 60-run stand for the sixth wicket.
Jadeja returned to dismiss Bresnan and Ashwin bowled Bopara, but Stuart Board and Graeme Swann were able to see England home.