India, whose win in Derby had set up the decider, recovered from 35 for five at the halfway stage to set a target of 123.
After looking well positioned, opener Sophia Dunkley fell just short of another 50 before stand-in skipper Amy Jones lasted only five balls. South East Stars batter Capsey, though, steadied the ship alongside Bryony Smith to see England over the line in the 19th over.
England, showing one change as Issy Wong came into the side for Lauren Bell, won the toss, with Jones electing to bowl first. After Jones missed a stumping chance to dismiss Shafali Verma to the second delivery of the innings, Wong struck to remove the opener with a knuckle ball which swung in, went off the batter's foot and back onto leg stump.
India soon also lost Sabbineni Meghana - who had made a half-century at Derby - for a duck as Danni Wyatt took a fine diving catch off Freya Davies. Dayalan Hemalatha was swiftly gone without troubling the scorers as Jones collected a thick edge from Sarah Glenn's opening over.
With India struggling to find boundaries, captain Harmanpreet Kaur (five) was the next out, clean bowled by Glenn as she came down the wicket. England successfully reviewed an lbw call against Sneh Rana (eight), Sophie Ecclestone's low delivery hitting on the back foot, as India slumped to 52 for six.
Jones then stumped Deepti Sharma, ending her revival attempts at a near run-a-ball 24, before wicketkeeper Richa Ghosh went on the offensive with three successive boundaries off Wong to push India towards a century.
Ghosh (33) was eventually halted when trapped lbw attempting to sweep Ecclestone in the penultimate over, India up to 103 for eight. Pooja Vastrakar finished with a flourish, unbeaten on 19 off 11, and Radha Yadav was five not out. Ecclestone claimed three for 25.
England opener Dunkley - whose unbeaten 61 helped guide England to a dominant nine-wicket victory in the opening match at Chester-le-Street - soon set about the run chase.
India eventually broke the partnership when Wyatt (22) was caught in the deep by Radha Yadav off Rana as England then moved on to 71 for one at the halfway stage.
After being frustrated by facing a maiden over from Yadav when on 49, Dunkley then lost composure as she was bowled by seamer Vastrakar when swinging for a boundary. India kept the squeeze on as Jones (three) lasted only five balls before Yadav removed her off stump, leaving the hosts suddenly stalling at 79 for three.
Capsey, though, soon settled any nerves as the 18-year-old made 38 off 24, with six boundaries, alongside Smith's unbeaten 13 to guide England safely home.
Additional reporting by PA.