Rahul plundered five sixes and 10 fours from 54 balls as India reached their target of 160 with 10 deliveries to spare.
India left-arm wrist-spinner Kuldeep Yadav took five wickets, including three in one over, as England struggled to a modest 159-8 from their 20 overs.
Jos Buttler continued his rich vein of form with 69 off 46 balls but the hosts faltered after a bright start and Yadav's inspired spell of 5-24 ripped out their middle-order.
After the early loss of Shikhar Dhawan, Rahul and Rohit Sharma shared a rapid second-wicket partnership of 123 and India were able to knock off the last few runs mainly in singles as they eased to a 1-0 lead in the three-match series.
India captain Virat Kohli praised the contributions of his match-winners.
"He's (Rahul) someone who has come a long way," Kohli told Sky Sports. "We want guys like him to step up, so other guys can play with more freedom. He's very hungry and it's a great sign for Indian cricket.
"He's (Yadav) going to be effective on any pitches we play on. When it turns, he's going to be even more lethal. He's very difficult to pick."
The second game is in Cardiff on Friday.
(Reporting by Ed Osmond, editing by Pritha Sarkar)
