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.
It seemed that loss to Sri Lanka was very much in the players' minds as they laboured to five for one after five overs - Danielle Wyatt, who had already been dropped by Thirush Kamini at slip, 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, driving Sharma for four for the first boundary of the innings. Edwards, who managed just one run from her first 20 balls, got in on the act too with a couple of cut shots, before driving Goswami down the ground.
The partnership added exactly 100 before Taylor was run out by Sharma going for a quick single, but Edwards kept rolling with successive fours off Reema Malhotra and Lydia Greenway was straight into her stride. She made 29 off 27 before hitting Goswami straight up in the air, Poonam Raut holding a simple catch.
That made it 166 for three in the 36th over, but with Katherine Brunt picking up where Greenway had left off, Edwards produced a neat late for a boundary - her 15th of the innings - to take her to 100.
Brunt's contribution had reached 21 when she cut a Gouher Sultana delivery up in the air and straight to Sharma in the 41st over.
The wickets continued to tumble as England looked to up the run-rate, 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.
Jenny Gunn (three) swiftly followed, miscuing to Malhotra at long-off off the bowling of Niranjana, from the final ball of the 45th over, and Heather Knight departed in the following over - run out for two by Goswami.
Laura Marsh managed a quickfire 13 from 11 deliveries before chipping to Goswami at long-on to hand Niranjana her second wicket in the penultimate over.