Jasprit Bumrah trapped Sibley lbw with an inswinging yorker in the final delivery of the day, but not before Root (128 not out) and opener Dom Sibley (87) had put the tourists in commanding position with a marathon double century stand.
England posted 263-3 at stumps, after electing to bat first on a flat pitch at M.A. Chidambaram Stadium.
Root’s century comes on the back of match-winning knocks of 228 and 186 in Sri Lanka.
The 30-year-old who made his Test debut in India in 2012, handled the spinners with aplomb as he swept and reverse swept to precision in his 197-ball knock.
Root struck 14 fours and a six.
The England skipper became the ninth man in world cricket to have scored centuries in their 100th Test joining former England skippers Colin Cowdrey and Alec Stewart, Australian Ricky Ponting, Javed Miandad and Inzamam ul Haq of Pakistan, West Indian Gordon Greenidge, South Africans Graeme Smith and Hashim Amla in the elite list.
Friday's effort was his third successive and 20th Test ton and termed it a “very special” knock. Root also appeared to have won his battle against Ravichandran Ashwin, smashing the off-spinner for a six before cramps set in.
Root put on 200 runs with Sibley after England slipped to 63 for two in the first session to nearly squander their strong start.
Sibley completed his second successive Test fifty after a cautious but steady start with opening partner Rory Burns. Left-hander Burns fell to Ashwin for 33 while attempting a reckless reverse sweep and offering a simple catch to Rishabh Pant just before lunch.
Bumrah, playing his first Test at home, struck soon after to trap new batsman Dan Lawrence lbw for a duck.
Root survived an early run-out chance while a couple of edges fell short of the fielders behind the stumps. He craftily eschewed the sweep for the first 50 balls of his innings, reaching 12 off 54 balls before skipping down the pitch and reverse-sweeping the spinners at will.
India, playing their first home series in 14 months since the COVID-19 pandemic struck last year, looked sloppy in the field with several misfields.
They bowled 11 no-balls, four of them by left-arm spinner Shahbaz Nadeem who was a late replacement for the injured Axar Patel.
Indian skipper Virat Kohli, back after missing three matches of the series win against Australia, desperately missed the injured Ravindra Jadeja.
Washington Sundar retained his spot at No. 7 as India opted for three finger spinners.
For England, Dom Bess retained his place ahead of Moeen Ali, while James Anderson was picked over Stuart Broad.
India have lost only one of the last 35 matches they have hosted and boast a record 12 successive Test series wins at home, including a 4-0 series victory during England's previous tour in 2016-17.
However, ominously England are the last team to have triumphed in India in 2012-13 and have arrived after blanking Sri Lanka 2-0 in their away series.