The right-hander responded to the backlash against England's 'Bazball' approach after their drubbing by 434 runs in the third Test, with an unbeaten 106 not out which brought England back into the game from a precarious 112-5 at lunch.
Root's own dismissal in Rajkot - playing a reverse scoop against Jasprit Bumrah - was seen as symptomatic of what is wrong with England's ultra-aggressive batting.
Ollie Robinson was also unbeaten after a useful cameo of 31, relieving the pressure on Ben Stokes, who was earlier left to rue his decision to bat as England lost the top half of their batting order in the frenetic first session.
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The hosts' 2-1 cushion in the five-match series allowed them to rest pace spearhead Bumrah, and Akash Deep became the fourth Indian to make his debut in the series.
The right-arm seamer impressed immediately, sending opener Zak Crawley's off-stump cartwheeling in his second over but his celebrations were cut short when the no-ball siren went off. He soon got over that disappointment by striking twice in three balls.
Akash dismissed Ben Duckett caught behind for 11 with an angled delivery that prompted a tentative prod from the opener.
Akash waited for confirmation that he had not overstepped and beat his chest in celebration.
Two balls later, Ollie Pope fell lbw for a duck.
Crawley went after Mohammed Siraj, hitting the bowler for three fours in a row and following that up with a huge six.
Enter Akash, who ended Crawley's run-a-ball 42 by hitting the top of his off-stump.
"I was upset with the no-ball not because it was my first Test wicket," Akash told the broadcasters afterwards.
"I was worried it could cost us some runs as Crawley was going after us. I was relieved to get rid of him soon."
Jonny Bairstow (38) has been unusually subdued in the series and he squandered another start by attempting a sweep shot against Ravichandran Ashwin only to be dismissed lbw.
Ravindra Jadeja dismissed Stokes lbw for three with the final delivery before the lunch break that stayed low.
With their top half back in the hut, England's capitulation on a spiteful pitch appeared only a matter of time.
But former captain Root had other ideas and combined with Ben Foakes (47) in a century stand denying India any wicket in the second session.
Siraj returned to remove Foakes and Tom Hartley after the tea break, but Root could not be denied his 31st Test hundred.
Root was a lot more judicious in his shotmaking, hitting nine fours in a patient knock.
England said leg-spinner Rehan was returning home for personal reasons.
