England's leading batsman in recent years, Root was his customary elegant self and made 124 off 180 balls, while Moeen Ali was one short of his fourth Test hundred when the stumps were drawn after 93 overs at the Saurashtra Cricket Association Stadium.
Root's effort was the first Test century by a visiting batsman in India since Michael Clarke's 130 at Chennai in February 2013. This was also the first time in the last 21 innings a visiting side crossed a 300 plus score in India.
Ben Stokes (19) was the other unbeaten batsman at stumps.
To India's good fortune, the well-entrenched Root was dismissed midway into the last session through a return catch by Umesh Yadav who bent low to accept the firm drive but then, in his enthusiasm, flicked the ball back over his head.
Luckily for the home team, which looked bereft of ideas on how to dismiss the classy batsman, the third umpire ruled in India's favour after Root stood his ground, indicating the pacer had not completed the catch.
Earlier, things had seemed bright for the hosts, who are seeking their third back-to-back Test series triumph and their first in four rubbers against the tourists, when they packed off England captain and their scourge Alastair Cook for 21 who was trapped leg before by Ravindra Jadeja.
Cook, dropped on zero off the third ball of the match by Ajinkya Rahane off Shami, later preferred not to review the leg before wicket decision given against him although replays suggested the ball might have missed the leg stump.
(REOPENS DEL31)
India grabbed three wickets in the first session after England commenced at the overnight 288 for five and then claimed the last two wickets within six overs after lunch.
Jos Buttler was the last man to be dismissed for 76, the second-highest scorer after the 112 made by debutant opener Keaton Jennings yesterday. He was bowled by Jadeja after he faced 137 balls and hit six fours and one six.
Ashwin, who had four scalps in his kitty yesterday, added another wicket by dismissing the tall number 10 batsman Jake Ball (31 off 60 balls) who added 54 runs with Buttler for the ninth wicket, a very useful stand.
Indian openers Rahul and Vijay started confidently against the pace attack of the visitors who tried to use the short ball to unsettle both without success. Vijay, who had got out on a few occasions in the series to the short ball aimed at his ribs, negotiated similar threats with more conviction.
Rahul, however, went for an ambitious drive against Moeen Ali on a track offering copious turn and was bowled through the gate for 24 after facing 41 balls. England had brought on their double spin attack -- Moeen and Rashid -- after only seven overs after pace duo of Anderson and Woakes began the proceedings.
Post tea, Vijay had one lucky moment when on 45 as he came out of the crease against Rashid, missed the ball which spun and bounced past wicketkeeper Bairstow. After that he completed his half century, the 15th of his 46-Test career, in 126 balls with the help of one six and five fours. He has hit six fours and two sixes in his unbeaten 169-ball knock.
Both Vijay and Pujara negotiated the spinning ball with aplomb, using their feet to meet the ball or by playing late.
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