Root smashed 18 fours in his unbeaten 321-ball 180-run innings, his fifth century of the year, to anchor the England innings.
The England skipper forged a vital 121-run partnership with Jonny Bairstow, before adding 54 and 58 with Jos Buttler (23) and Moeen Ali (27)
Earlier, with Root going strong, England scored as many as 97 and 98 runs in the first two sessions, signalling the plight of the Indian bowling attack.
Ishant Sharma (3/69) and Mohammed Siraj (4/94) did well to bring India back in the game.
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They are cheaper to run. They can be simpler to manufacture. And of course, they are far better for the environment, playing a crucial role in hitting our targets to cut carbon emissions.