Edwards' knock helped her side post 272 for eight from their 50 overs, with Katherine Brunt (four for 29) then the pick of the bowlers as England limited the hosts to 240 for nine despite an unbeaten 107 from Harmanpreet Kaur.
Edwards needed 53 to surpass the previous record of 4,844 held by Australia's Belinda Clark and, after a slow start, she did that and more, claiming her seventh ODI ton to help England recover from their opening defeat by Sri Lanka.
Today's result left Group A wide open, with all four teams having one won and lost one of their first two games.
It seemed the opening loss to Sri Lanka was very much in the England players' minds as they laboured to five for one after five overs - Danielle Wyatt (two) the woman to fall as she clipped Jhulan Goswami to Amita Sharma at midwicket.
It was perhaps what England needed, though, as Sarah Taylor came in and began to play some shots. Edwards got in on the act too, and the partnership yielded exactly 100 before Taylor (35) was run out by Sharma going for a quick single.
But Edwards kept rolling and Lydia Greenway was straight into her stride, making 29 off 27 balls becoming Goswami's second victim.
Brunt then picked up where Greenway had left off, while Edwards' 15th boundary of the innings moved her onto 100. Brunt's contribution had reached 21 when she fell to Gouher Sultana, with Edwards the next to go when she took off for a risky single after pushing to cover and was run out by Nagarajan Niranjana.
The late wickets continued to tumble as England looked to up the run-rate, Laura Marsh's 13 from 11 balls boosting the total before her dismissal in the penultimate over.
India's response got off to a shaky start, the home team struggling to 29 for three in the eighth over. Brunt saw off Thirush Kamini (10) and captain Mithali Raj (eight) before Anya Shrubsole trapped Poonam Raut lbw for four.
Kaur and Karu Jain (56) steadied the ship for India with a 106-run fourth-wicket stand before the latter holed out to Marsh at backward point off the bowling of Arran Brindle.
Goswami (19) soon followed suit before Reema Malhotra (17), Sharma (nought) and Niranjana (nought) fell in consecutive balls - from Brunt and Wyatt, with the score on 225 - to snuff out any hopes of a late victory charge.