Mohammad Shami dismissed Moeen Ali (117) in the early overs of the second day of the first test against England at the the Saurashtra Cricket Association Stadium here today.
Joe Root (82 not out) then added another 99 runs for the sixth wicket with Bairstow (46) who was dismissed by Shami.
England now seems to be in a dominating position in the first Test as the visitors have amassed 447 runs with another four wickets remaining.
Yesterday, Root provided the desired start with his 11th Test century, helping England finish the opening day of the first cricket Test at a solid 311/4 here on Wednesday.
Indian bowlers were made to toil as England began their campaign on a promising note.
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.
The 25-year-old Root's maiden ton on the Indian soil was laced with one six and 11 fours, while Ali struck nine boundaries. The duo shared 179 runs for the fourth wicket to bail England out from a tricky 102/3.
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.
India, incidentally, had not taken the second new ball till stumps. Pacer Mohammed Shami going off the field with a hamstring injury was not good news for India. The seamer returned later, but clearly looked in pain.
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.
The other two wickets that fell early in the day were grabbed by off-spinner Ravichandran Ashwin who sent off debutant opener Haseeb Hameed for 31, earning a leg before verdict that was reviewed by England without success and Ben Dockett for 13, caught at slip by Rahane in the last over before lunch.
But thereafter one-down Root, batting fluently and using his feet beautifully against the spinners, and Ali, who played the ideal foil, took centrestage as they laid the foundation for a huge first innings total.
(With inputs from PTI)