Led by Jofra Archer’s 3-23, England restricted India to 124-7.
Jason Roy and Jos Buttler opened with 72 and England won at 130-2 with 27 balls to spare.
Roy and Buttler raised 50 runs in the first six overs. Roy was out for 49, trapped leg before wicket by Washington Sundar, and Buttler made 28.
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Jonny Bairstow was unbeaten on 26 and Dawid Malan on 24 after clubbing a winning six off Sundar.
Archer took a wicket off his second delivery when Lokesh Rahul played the fast bowler back onto his stumps. Hardik Pandya and Shardul Thakur fell in the paceman’s last over off successive deliveries.
Captain Virat Kohli, who struggled in the preceding 3-1 victory in the test series against England, fell for 0 to legspinner Adil Rashid as India fell to 3-20 in the first five overs and couldn’t recover.
Shreyas Iyer hit a fighting 67 off 48 balls in an otherwise below-par batting effort by India, for whom star opener Rohit Sharma is being rested for the first two games.
The second T20 of five is on Sunday.