Batting first, England posted 321-8 from their 50 overs, with Jason Roy, Jonny Bairstow and Ben Stokes all passing 50, while Hardik Pandya was the pick of the Indian bowlers, claiming 3-49 from his ten.
In response, Virat Kohli made 55 before he was caught behind off Stokes, and despite Kedar Jadhav (90) and Pandya (56) pushing India close, an excellent final four balls from Chris Woakes salvaged the confidence boosting win for England.
Roy shines once more before Stokes smokes Indian attack all over Kolkata as England post 300+ once more
In what has been a constant during this three match series, Jason Roy has provided England with a more than solid platform at the top of their innings. His third half century of the series, this time 65 from 56 balls was crucial in a 98-run opening stand alongside Sam Billings who replaced the injured Alex Hales before falling to Ravindra Jadeja for an out of sorts 35.
England's other change saw Jonny Bairstow grab his opportunity with two hands, making 56 from 64 balls and doing so in an assured fashion which will have reminded the selectors of his white-ball prowess going forward.
Eoin Morgan backed up his exquisite ton in the second ODI with 43, which included three maximums, before falling to Pandya in an inspired spell of bowling which also saw him claim the scalps of Bairstow and Jos Buttler who made just 11.
In a repeat of the first game, Stokes was England's go-too man in the final overs and he hit six boundaries in a 39-ball 57 which will have again caught the eye of IPL franchises, and thanks to 34 quickfire runs from Woakes, England powered past 300 once more and set India 322 for a series sweep.
England knock over top five despite loss of Willey to shoulder injury
As has been the case for the entire series, England's bowlers have had the better of India's openers and within six overs of the chase starting, both Ajinkya Rahane and KL Rahul were back in the hutch. Rahane was first to go for one in what can be best described as rusty innings before he was bowled by David Willey, with Rahul following a couple of overs later for 11 after skying a delivery from Jake Ball.
The best chaser in world cricket was then at the crease and just as he looked to be off in pursuit of another total of 300+, Eden Gardens fell silent as Stokes caught the edge of Kohli's bat, with Buttler pouching the easy chance to dismiss the skipper for only 55.
India's heroes from the second ODI were next to fall, with Yuvraj Singh finding Billings on the boundary after pulling a delivery from Liam Plunkett, before MS Dhoni nicked Ball behind to Buttler, leaving India in a bit of strife at 173-5.
Woakes holds his nerve as Jadhav and Pandya threaten to complete rout
A worrying trend for England had been their lack of ruthlessness when in positions of strength during the series and this continued through to the final game as India staged a fightback which nearly saw them claim an unlikely victory.
A 100-run partnership between Jadhav and Pandya following the Dhoni dismissal was exactly what India needed, and it came at a good pace too with Pandya smashing four fours and a pair of sixes before his 43-ball knock of 56 was brought to an end by Stokes who ripped through his defences.
On the scene of his most infamous day in international cricket, Man of the Match Stokes was inspired by the opportunity to answer a few demons, and after Woakes had removed the dangerous Jadeja, the Durham all-rounder had Ravi Ashwin caught with his penultimate delivery of the game to leave India still needing 25 from 13 balls.
Jadhav had designs on stealing Stokes' award, and after taking seven from Ball in the 49th over, he plundered a six and a four to open the final over from Woakes and had seemingly put his side in the driving seat with the target now reading six from four balls.
Woakes then hit back, showing balls of steel to end the game with four straight dots which included the wicket of Jadhav two balls from the end as England claimed a moral boosting win ahead of the three-game T20i series which will bring the curtain down on a tough tour.