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. Teams: India: Mahendra Singh Dhoni (c), Shikhar Dhawan, Ajinkya Rahane, Virat Kohli, Ambati Rayudu, Suresh Raina, Ravindra Jadeja, R Ashwin, Bhuvneshwar Kumar, Mohammed Shami, Umesh Yadav.
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.
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. Jadeja (0/66) had an off-day.
England skipper Alastair Cook (46 runs) and Alex Hales (4) looked for a good start to put India under some pressure, but it wasn't meant to be despite a quick get away.
Hales was aggressive and miscued a 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.
But despite these lives, he could not even get to his half-century and was gobbled up by Dhoni as he tried to sweep Raina in the 20th over.
Eoin Morgan (14) then came to join Root in the middle but his poor run of form continued and he was stumped by the Indian skipper off Ashwin in the 29th over.
The 100-run mark had come up in the 24th over but only 26 runs were added by the English batsmen in this interim of play spanning nine overs.
It heaped the pressure on new batsman Buttler but he responded well enough to put on a century-stand for the fifth wicket.
Root then reached his fifty off 68 balls, with six fours, in the 32nd over. The two batsmen looked to take more risks as they put on 50-runs off just 43 balls.
For the first time in the series, India's spinners weren't able to dictate terms and it could be seen most in the
second powerplay as Root-Buttler took 55 runs off those five overs.
England's 200-run mark came up in the 40th over thus and two overs later Root-Buttler celebrated a 100-run partnership coming off only 75 balls.
But in the 43rd over, the latter was run-out by Dhoni as he failed to locate the ball after trying a sweep, falling
painfully short of a well-deserved half-century.
But Root rallied on, scoring the first-ever ODI hundred by a Yorkshire batsman at his home-ground, getting to the land-mark in the 45th over.
He had faced 105 balls, hitting nine fours as well as two sixes, to get there. He added another boundary and six to his tally, looking for some quick-scoring before the end but perished in the bid to do so, finally caught by Ashwin at short fine-leg off Shami.
Stokes (33 not out), along with Chris Woakes (9) and James Tredwell (8 not out), hit out in the last few overs as India conceded 143 runs in the final 15 overs.
India 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 Stokes coming in for them.
England: Alastair Cook (c), Alex Hales, Moeen Ali, Joe Root, Eoin Morgan, Jos Buttler†, Ben Stokes, Chris Woakes, James Tredwell, Steve Finn, James Anderson.
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: Mahendra Singh Dhoni (c), Shikhar Dhawan, Ajinkya Rahane, Virat Kohli, Ambati Rayudu, Suresh Raina, Ravindra Jadeja, R Ashwin, Bhuvneshwar Kumar, Mohammed Shami, Umesh Yadav.