Chasing 249 for victory after Jos Buttler had scored 52 and Jacob Bethell 51 to boost England's total following a wobble midway through the innings, India reached their target on Thursday with 68 balls to spare.
Gill overcame cramp to make 87 and take India close to the finish line on a two-paced, turning wicket at Nagpur's Vidarbha Cricket Association Stadium after Patel scored 52 in a 108-run stand for the fourth wicket.
To start the series that's acting a warm-up for the Champions Trophy, Yashasvi Jaiswal came into India's XI after Virat Kohli was ruled out due to a sore right knee.
But Jaiswal was out for 15 following a probing early spell by Jofra Archer while out-of-form captain Rohit Sharma fell for two to Saqib Mahmood.
Iyer blasted two consecutive sixes off Archer in the seventh over en route to his entertaining half-century and after he departed for 59, Gill played a controlled knock with some exquisite shots on both sides but holed out to Mahmood late on.
Ravindra Jadeja (12no) and Hardik Pandya, who was unbeaten on nine, then took the hosts home.
"We're pretty happy because we knew we were coming back after a long time to this format," Rohit said of his team's first match in 50-over cricket since August.
"We wanted to quickly regroup and understand what is to be done. We didn't start well with their openers putting pressure on us, but the way we came back was superb.
"This is a slightly longer format where you have time to come back. When things start to go away from you, it doesn't mean it will keep going away."
England had earlier elected to bat after winning the toss and went into attack mode when Phil Salt plundered 26 runs in the sixth over bowled by Harshit Rana, before the tourists cruised to 0-71 after eight overs.
India struck against the run of play when a mix-up led to Salt being run out for 43 while opening partner Ben Duckett was out for 32 after Jaiswal produced a brilliant running catch to hand fellow ODI debutant Rana his first wicket.
Rana then dismissed Harry Brook for a duck three balls later before Joe Root, who returned to the ODI fold for the first time since England's ill-fated World Cup title defence in 2023, was trapped lbw by Jadeja for 19 shortly after.
Skipper Buttler and Bethell revived England's innings with battling half-centuries but the hosts kept taking timely wickets to ensure their opponents were bowled out for 248, with Jadeja picking up 3-26 and Rana finishing on 3-53.
"Obviously disappointed not to win," Buttler said.
"We got off to a fantastic start, the two guys (Salt and Duckett) were very aggressive in the powerplay. Losing four wickets so close together put us back.
"When you see the way the wicket played, another 40 or 50 runs could have been crucial."
The second ODI takes place in Cuttack on Sunday before the finale in Ahmedabad on February 12.
It will be followed by the eight-team Champions Trophy beginning February 19 in Pakistan and the United Arab Emirates.
