Root struck 113 runs as England put on board a challenging 294 for seven and then bowled out the visitors for 253 in 48.4 even as India won the series 3-1 on the back of their previous victories.
India, who dominated the series with their consistent show, opted to bowl but Root's hundred ensured that the home side scored their highest total of the series.
Root faced 108 balls and hit 10 fours along with three sixes in his magnificent innings. He added 108 runs off just 71 balls with Jos Buttler (49) for the fifth wicket scoring at impressive 8 runs per over.
In-form Indian opener Ajinkya Rahane (0) struggled today as he was dismissed for a nought but other batsmen, who got starts were guilty of not converting on an easy batting strip. In a splendid rearguard action, Ravindra Jadeja hit an aggressive 87-run knock but was it was too late and only reduced the defeat margin.
The southpaw hit nine fours and two sixes in his entertaining 62-ball innings. Young batsman Ambati Rayudu came up with a fighting 53-run knock off 65 balls in India's resistance but his promising innings was cut short by Ben Stokes.
Opener Shikhar Dhawan scored 31 off 44 balls before being castled by Moeen Ali, who also got key wicket of Suresh Raina (18) as the off-spinner played a crucial role in turning the tide in his side's favour.
Till Mahendra Singh Dhoni was at the crease, India had their hopes alive but once the skipper fell in a bizarre fashion, it was a matter of time for England to complete the win.
Dhoni chased a widish ball from Steven Finn and sent it straight to Stokes, gifting away his wicket after making 29. After that it was Jadeja, who kept England fielders busy, but could not pull off miraculous win.
For England, pacer troika of Stokes (3/47), James Anderson (2/39) and Steven Finn (2/37) shared seven wickets between them while Ali took two wickets.
Root scores 113
Root sparkled with his second ODI hundred as England's batting finally came good. Root's second ODI hundred helped England reach 294/7 in their allotted 50 overs. Root scored 113 runs (108 balls, 10 fours, three sixes) as the home side scored their highest total in four ODIs so far.
Root added 108 runs off just 71 balls with Jos Buttler (49) for the fifth wicket scoring at a break-neck pace of 8 runs per over.
For India, Mohammad Shami (2-52) was again the best bowler on display, while Bhuvneshwar Kumar (1-45), Umesh Yadav (1-46), R Ashwin (1-49) and Suresh Raina (1-32) also took a wicket each. Ravindra Jadeja (0-66) had an off-day.
Earlier, Dhoni once again won the toss and opted to field first. The visitors made one change, bringing in Umesh Yadav for Dhawal Kulkarni, while England made two changes to their line-up from the previous game.
Gary Ballance and Harry Gurney were left out with James Tredwell and Ben Stokes coming in for them. Alastair Cook (46 runs, 64 balls, 6 fours) and Alex Hales (4) opened the innings then, looking for a good start to put India under some pressure, but it wasn't meant to be despite a quick getaway.
Hales looked to be aggressive and played a false pull shot to be caught at mid-wicket off Yadav in the 4th over. Moeen Ali (9), given a promotion after his blitzkrieg fifty in the previous match, was out three overs later, again looking to be too aggressive as he smacked the ball straight to third man.
It was looking like routine for England at 39/2, but Cook and Root rebuilt the innings. They added 52 runs for the third wicket, with the English skipper enjoying quite a bit of luck during his stay at the wicket.
He had nicked the ball twice through the absent second slip - on 9 in the third over and then at 19 in the seventh over.