India captain Shubman Gill top-scored with 80, before retiring hurt with his side needing 110 runs from 24.2 overs, and Axar Patel hit 57 as they reached their target of 259 comfortably on a balmy evening.
Washington Sundar (52) wrapped up the match with a flourish, hitting a six that also brought up the 100 partnership with Patel, for a final score of 262-4 off 45.2 overs.
Patel had earlier taken four wickets in a man-of-the-match performance by the left-arm spinner.
"The way the T20 series went, I think this is the perfect start for us," he said.
Top-order batters Virat Kohli and Rohit Sharma had both gone cheaply, the first lbw for five to Jofra Archer and the latter caught by England captain Harry Brook for 11, but rising hopes of a home victory were soon dispelled as the runs piled up.
Gill said he had suffered cramp but was already feeling better: "I wanted to finish the job for the team, but I had to come out. Very glad with the result," he added.
England had started the day by winning the toss and opting to bat but lost both openers and Brook in the space of six balls to slump to 64-3 after a 61-run opening stand.
Jacob Bethell was first out, caught by a diving Washington Sundar off Gurnoor Brar, and fellow-opener Ben Duckett (43) followed three balls later when he was caught by Jasprit Bumrah on the boundary.
Brook was caught for one by Rohit at slip off Bumrah's first delivery of his second spell, with Jos Buttler coming to the crease in his 200th ODI.
Buttler went for five, caught by Brar off Prasidh Krishna, and England were reeling after Sam Curran was out for a duck at 80-5.
The collapse continued when Will Jacks was caught one-handed by a diving KL Rahul, but Liam Dawson and Joe Root, dropped on seven by Shivam Dube, dug the home side out of a hole with a 121-run partnership.
Dawson departed for 68 off 83 balls, his highest score in international cricket, while Root battled on to 76 not out.
Nottinghamshire seamer Josh Tongue, making his ODI debut, was bowled middle stump by Patel with 13 balls remaining to close out England's innings.
"I think we lost five for 20 in that middle period, which is always going to put us on the back foot," said Brook.
"We would have definitely liked to have played slightly better in that period of the game."
The match was England's first since Brendon McCullum was sacked as head coach of the test team.
Two more ODIs follow, in Cardiff on Thursday and at Lord's on Sunday.