The 30-year-old Root became the first player to notch up a double ton in his 100th Test on the way to his 218 off 377 balls, while Ben Stokes hit a counter-attacking 82 off 118 balls, studded with 10 fours and three sixes.
SCORECARD | As it happened
Root’s fifth Test hundred was laced with 19 hits to the fence and two maximums, one of which helped him to reach the milestone.
At the draw of stumps, Dominic Bess (28) and Jack Leach (6) were at the crease at the MA Chidambaram Stadium.
Resuming the day at 263 for three, England amassed 191 runs in the first two sessions before India fought back with four wickets in the last session.
Root shared a 124-run partnership with Stokes for the fourth wicket, before forging another 86 with Ollie Pope (34) to put England in a commanding position.
England 1st innings: 555 for 8 in 180 overs (Joe Root 218, Ben Stokes 82, Dominic Sibley 87; Jasprit Bumrah 2/81, Ishant Sharma 2/52).