At the other end, Sibley, who provided admirable support to Root and anchored the innings, mixed caution with aggression, is well poised to score a century, but fell in the last over of the day after scoring 87 (286 balls, 12x4) as the duo added 200 runs for the third wicket in 63.5 overs, to put England firmly in command.
Root became the ninth batsman to score a century in his 100th test and the second England cricketer after former captain Alec Stewart.
Except for the dual success just before lunch break, when opener Rory Burns (33, 60 balls 2x4) fell to R Ashwin due to poor shot selection and medium pacer Jasprit Bumrah trapped Dan Lawrence (0), it was a hard toil for the Indian bowlers on a pitch, which was slightly on the slower side, but good for batting under extremely hot and humid conditions.
However, relief came in the form of Bumrah, who gave some opening by getting rid of well set Sibley in the last over of the day on an otherwise tough day for the home team.
After a steady start when Sibley and Rory Burns added63 for the opening wicket by negotiating the new ball bowlers and handling the spinners with aplomb, the two quick wickets, just 10 minutes before lunch, pegged the visitors back.
But, on resumption Root, who tackled the spinners with aplomb in the recent two test series against Sri Lanka in which he scored 426 runs series, continued in the same vein.
Sibley, on the other hand showed plenty of character as the duo steadied the innings by taking singles and twos, with occasional boundaries when the bowlers pitched short or offered width.
Both the batsmen displayed sound technique against the spinners, used their feet well, and used the sweep to good effect.
Runs came fast in the post-tea session as both of them cut, drove and pulled, giving no chance for any bowlers to make any inroads.
The first session yielded 67/2 in 27 overs, second 73 in 30 overs and the final session 123/1 in 32.3overs.
Indian skipper Virat Kohli kept shuffling his bowlers but the duo kept them at bay.
Ishant Sharma bowled with his heart out, maintain the fabulous line and also got some reverse swing. Bumrah too tested the batsmen with short pitched deliveries and yorkers, but Root and Sibley played with soft hands.
Ashwin occasionally managed to get some turn and bounce to keep the batsmen in right leash, while offie Washington Sundar and left arm spinner Shahbaz Nadeem could not make any impact on the batsman.
As the partnership blossomed, Root outscored his partner and reached his century off 164 balls and celebrated the milestone by punching his firsts in the air, as the England dressing room and Indian cricketers applauded.
The second new ball was taken after 81 overs, but runs flowed steadily as the England batsmen ended the day ona high, having put the team in a firm position, setting the stage for a big total.
Following is the scoreboard:
England (first innings): Rory Burns c Rishab Pant b R Ashwin 33 Dom Sibley lbw Jasprit Bumrah 87 Dan Lawrence lbw Jasprit Bumrah 0 Joe Root (batting) 128
Extras: (LB-4, nb-11) 15 Total: 263 for three in 89.3 overs.
Fall of wickets: 1-63, 2-63, 3-263.
Ishant Sharma 15-3-27-0
Jasprit Bumrah 18.3-2-40-2
R Ashwin 24-2-68-1
Shahbaz Nadeem 20-3-69-0
Washington Sundar 12-0-55-0 (UNI)