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, Indian skipper Mahendra Singh 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.
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.
Ben 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: Mahendra Singh Dhoni (c), Shikhar Dhawan, Ajinkya Rahane, Virat Kohli, Ambati Rayudu, Suresh Raina, Ravindra Jadeja, R Ashwin, Bhuvneshwar Kumar, Mohammed Shami, Umesh Yadav.
England: Alastair Cook (c), Alex Hales, Moeen Ali, Joe Root, Eoin Morgan, Jos Buttler, Ben Stokes, Chris Woakes, James Tredwell, Steve Finn, James Anderson.