Kohli stroked his way to a career-best 211 and was brilliantly supported by Ajinkya Rahane, who also notched up his highest score of 188 as the home team gained a clear upperhand on a pitch that will only get difficult to bat with passage of time.
At stumps, New Zealand were 28 for no loss with Martin Guptill (17 batting) and Tom Latham (6 batting) at the crease.
The duo decimated the New Zealand attack to pile on a huge fourth wicket partnership of 365 - the highest-ever for India for the fourth wicket against all teams.
When Virat Kohli declared half-an-hour before close, Rohit Sharma (51 not out in 63 balls) and Ravindra Jadeja (17 not out) were at the crease after adding a quick-fire 53 runs in 59 balls for the unbroken sixth wicket.
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Sharma cracked his third successive half-century of the series and struck 2 sixes and three fours.
It was the second double century by Kohli in the space of six Tests and three months.
These two batsmen's complete domination of the clueless New Zealand bowling attack enabled India to add 98 runs in 30 overs in the second session after they had added 91 runs in the pre-lunch session after resuming at the overnight 267 for 3.
Both batsmen exerted complete sway over the visitors' attack and were hardly beaten before they fell early in the post tea session.
(REOPENS DEL 66)
India, who lost the advantage of the toss at home for the first time after eight Tests, also let themselves down with sloppy close-in catching, grassing three in all, to let England off the hook.
Catches were dropped off Cook and Haseeb Hameed was let off by Murali Vijay in the slips off Yadav in the sixth over. Cheteshwar Pujara, at short leg, let the ball through his legs when Ali turned Ashwin after completing his half ton.
The major part of the day belonged to Root who had an average in excess of 100 in six previous Tests against India but had played just one Test prior to today's game.
He looked unflappable, settling first and then milking the bowling with singles and two runs, and the occasional boundaries.
In the company of Ali, who notched his first plus-50 score against the hosts and ninth overall, Root rebuilt the innings.
The not out decision by on-field umpire was reviewed by the Indians but replays showed the ball kissing the leg stump and the original not out decision remained.
Earlier, skipper Virat Kohli rung in bowling changes at both ends in order to break the fourth-wicket stand between Root and Ali, but all came to naught due to diligent batting by the duo.
The hosts' bowling also appeared quite thin on a track that was easy-paced and easy to bat on. The non-availability for some period of the day of Shami as a bowler, who looked far more impressive than his pace bowling partner Yadav, was a big handicap.
quickly before the visitors fought back through the ninth wicket stand between Buttler and Ball.
The first session of play was eventful, with the ball turning sharply and DRS called for on quite a few occasions by the home side.
India could have dismissed England had their catching been a little sharper on the turning track. Ashwin had Stokes top-edging in the very first over of the morning, but backward square leg fielder Bhuvneshwar Kumar reacted late to the opportunity and allowed the ball to hit the turf well in front of him.
The wicket took Ashwin's tally from the innings to five, the 23rd time in 43 Tests that the 30-year-old off spinner had performed the feat. It also broke the sixth wicket partnership between Stokes and Buttler that was threatening to becoming a big stand.
But Jadeja got rid of the other batsman -- Woakes -- in his seventh over of the morning when he got the batsman to edge low to Patel with a ball that turned sharp.
Buttler was lucky as he edged Ashwin close to Kohli in slip when on 40 and it needed Jadeja to remove Rashid at the other end with an arm ball that struck the off stump as the batsman left it by shouldering his arms.
Buttler went on to complete his half century in 106 balls and take England to 400 all out.