Joe Root's unbeaten 99 in Cardiff on Thursday set up a winner-takes-all contest and England were halfway there when Duckett's magnificent century was the bedrock of a record-breaking total of 3-387.
The best ever List A score at Lord's was helped by 91 from new ODI opener Jacob Bethell before Root's latest fifty was backed up by Jos Buttler's blistering 13-ball innings of 41.
In reply, Rohit Sharma blasted an equally stunning 138 to become the first India player to score an ODI hundred at the historic venue, but he was bowled by Bethell to flip the momentum at 2-260.
Virat Kohli had already picked up the baton after Shubman Gill's 77 and scored fifty on what may be his final innings in England, but two wickets for Sam Curran in the 44th over on his way to 4-75 further turned the screw.
Brook's team eventually restricted India to 7-360 to make it five wins out of six white-ball matches.
Earlier, the first of 13 Bethell boundaries came from an inside edge off Prasidh Krishna but he then survived a run-out chance on 25 before Prince Yadav's next delivery was pulled over deep square leg for six.
Bethell's 51-ball fifty brought up the hundred partnership with Duckett, who reached his own half-century with a cut for four. But Bethell eventually picked out Sharma and fell nine short of three figures.
Duckett brought up a fourth ODI hundred before Yadav's slower ball finally accounted for the Nottinghamshire opener on 141 leaving Root and Buttler to produce the late fireworks.
Root's reverse sweep for four off took him beyond his own past record of 309 runs without being dismissed in ODIs and he finished 74 not out.
Buttler then heaved Brar for six during a 23-run over which was followed by two more maximums back past Krishna, which took England to 3-387.
Sharma strolled out for the India innings amid speculation this could be his final match. Gill beat him to fifty but he was pinned lbw for 77 off Adil Rashid.
Back-to-back sixes off Tongue took Sharma into the nineties and a slog-swept over deep midwicket earned a richly deserved century.
Sharma finally exited bowled for 138 before Curran's two 44th-over scalps of Ishan Kishan and Shreyas Iyer knocked the stuffing out of India, who lost Kohli (74) and ended on 7-360.
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