Chasing 218 from 43 overs under the Duckworth/Lewis system after an hour's rain break in the day-night match, England survived a wobble in mid-innings to get over the line with seven balls to spare.
England lead 2-0 in the five-match series after the first game was rained out. The teams meet again at Lord's on Sunday and in Cardiff next Friday.
World Cup champions India, who lost their place at the top of the world rankings during a 4-0 whitewash in the test series, rallied from 58 for five to reach 234 for seven from their 50 overs.
All-rounder Ravindra Jadeja, an injury replacement for Gautam Gambhir, stroked the ball beautifully to score 78 from 89 deliveries. He added 112 with captain Mahendra Singh Dhoni (69) and 59 from 31 balls with Ravichandran Ashwin (36 not out).
Alastair Cook asked India to bat after winning the toss and won an immediate reward when Ajinkya Rahane, who had scored 155 from 120 balls in his three previous one-day internationals, was dismissed without scoring, caught behind prodding at James Anderson's fourth delivery of the day.
Anderson then ran out Rahul Dravid (2), swooping from mid-off to pick up the ball and throw down the stumps at the batsman's end in one motion.
Dravid, who had been late starting after Parthiv Patel had pushed the ball into the off and then hesitated before running, looked distinctly unimpressed with his partner's calling, swishing his bat in irritation as he to the pavilion.
Patel did not linger, departing for three when Anderson uprooted his off-stump and Virat Kholi (7) edged Anderson to give wicketkeeper Craig Kieswetter his second catch and compound India's misery.
Dhoni smacked his second ball for four and Suresh Raina launched Anderson into the crowd for the only six of the innings. Raina reached 21 before he tried to swipe Broad to leg and was caught behind.Read more
