Chasing 322 for victory, the Virat Kohli-led India side ended on 316-9 in their allotted 50 overs, courtesy half-centuries from Kedar Jadhav (90 off 75), Hardik Pandya (56 off 43) and captain Virat Kohli (55 off 63).
Stokes was the most successful bowlers from the visitors as he claimed three, whereas pacers Chris Woakes and Jake Ball picked two wickets each.
Another milestone for MS Dhoni
Earlier, the visitors after being put into bat, scored 321 for eight in their 50 overs, with Stokes scoring an aggressive half-century.
The 25-year-old smashed an unbeaten 57 off 39 balls, and there were also half-centuries from Jason Roy and Jonny Bairstow.
England’s innings started brightly with a 98-run opening stand between Roy (65) and Sam Billings (35) before the Indian bowlers came back with regular strikes.
Paceman Hardik Pandya claimed three wickets while left-arm spinner Ravindra Jadeja got two on a lively pitch at Kolkata's Eden Gardens Stadium.
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Jadeja sent both openers back to the pavilion, dismissing Roy for the third time in the series after the batsman's third successive ODI fifty.
Skipper Eoin Morgan, who struck a valiant 102 in England's second loss in Cuttack on Thursday, once again looked like he would pilot the innings with some assured hitting.
The left-hander shared an 84-run third-wicket partnership with Jonny Bairstow (56) before Pandya rattled the England middle order.
Morgan, who hit two fours and three sixes during his 44-ball stay, was out for 43 against the run of play after flicking a catch to Jasprit Bumrah at short fine leg.
Bairstow, who came into the side in place of the injured Alex Hales, survived a scare after he was caught at third-man off Bumrah on 28 off a no ball.
Bairstow went on to register his third ODI fifty but failed to convert it into a big score when he fell to Pandya, who finished with figures of 3-49.
But Stokes ensured the efforts of the top order were not in vain. He smashed four fours and two sixes to help the visitors put on 58 in the final five overs.
His 73-run seventh-wicket stand with Chris Woakes (34) was crucial in England's final push to get the score well past the 300-run mark.
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