On a cracked surface offering significant early assistance for India's bowlers, Ben Stokes' dismissal to a Ravindra Jadeja grubber left England on 112 for five at lunch after debutant Akash Deep's three-wicket haul.
But Root, averaging 12.83 after the first three matches, ended his lean patch with a battling 106 not out, which included a 113-run stand with Ben Foakes, as England went to stumps on 302 for seven.
What was striking about Root's 31st Test hundred, brought up off 219 balls, was its orthodoxy following criticism for some unconventional dismissals recently – especially his reverse ramp in Rajkot last week, which was a sliding doors moment in England slipping 2-1 down in the five-match series.
Whether he is suited to England's 'Bazball' approach has been the subject of much debate in the last few days but Root showed the virtue of patience here.
There were some sweetly-timed drives through the covers as well as his characteristic late cuts and shots square of the wicket as the Yorkshireman registered the slowest ton of the Stokes and Brendon McCullum era.
Root has given England a fighting chance after Deep ensured the rested Jasprit Bumrah was not missed at first, exploiting the variable bounce that was a theme throughout the day and some early movement.
Stokes had no hesitation in batting, as is customary upon winning the toss in India, despite wariness over a track he described as "interesting". What followed was a helter-skelter opening session as England went at 4.63 an over and lost five wickets, while two of India's five reviews were successful.
England's openers were routinely beaten on the outside edge and Zak Crawley had his off stump uprooted on four but it was found Deep had over-stepped. Deep did not have long to wait for a maiden Test wicket, though, as a searching delivery nipped away and grazed Ben Duckett's outside edge on 11.
Ollie Pope lasted two deliveries as India overturned a not out leg-before verdict and an eventful over saw Root survive the hosts' review for lbw first ball after getting fractionally outside the line of off stump.
Crawley then Jonny Bairstow counter-attacked, with both finding success against the expensive Mohammed Siraj.
But Crawley departed for a run-a-ball 42 when Deep's in-ducker snaked through the gate and kissed the off bail, while Bairstow was lbw on review for 38 after missing a slog sweep off Ravichandran Ashwin, who claimed his 100th Test wicket against England.
The tourists' cause worsened on the stroke of lunch when Stokes was lbw to an ankle-high shooter from Jadeja, the England captain throwing his head back and laughing ruefully as he began to trudge off before the umpire had raised his finger.
A frenetic morning gave way to a sedate afternoon as Root and Ben Foakes settled for steady accumulation. The pitch did not have as many demons upon the resumption and while the odd one kept low, the English pair were alert to the danger.
There were just seven boundaries between lunch and tea after 13 fours and two sixes in the opening session but India's often poor ground fielding allowed Root and Foakes to regularly rotate the strike.
Root went seamlessly to his first fifty in seven innings, after which Foakes, whose first boundary came with a drive off Kuldeep Yadav from his 66th ball, pushed the accelerator by taking 18 off an Ashwin over, including a big blow over the leg-side for six.
Foakes fell three short of a fifty after tamely chipping to midwicket, ending a 113-run stand with Root, while Siraj had his second wicket by knocking back the off-stump of Tom Hartley for 13.
Root, whose first and only reverse sweep came when he was on 76, kept going and moved to three figures with drive through the covers off Deep for his ninth four.
He celebrated the milestone in understated fashion by kissing the badge on his helmet and raising his bat as his team-mates, led by a grinning Stokes, celebrated enthusiastically on the balcony.
Root shared an unbroken 57 with Ollie Robinson, who should have been out on eight but India had burned their reviews. Instead Robinson, making his first appearance of the series, contributed 31 not out, taking England past 300 with a dismissive swipe for four off Yashasvi Jaiswal's last over of the day.
