Bairstow was unbeaten on 66 at the break while Jos Buttler was batting on 38 at the other end.
For India, Mohammed Shami, Umesh Yadav, Jayant Yadav, Ravichandran Ashwin and Ravindra Jadeja took a wicket each.
Coming together at the fall of Ben Stokes, Buttler and Bairstow added 61 runs between them to help restore some measure of respectability to the England scoreboard.
The Punjab Cricket Association I.S. Bindra Cricket Stadium has been a lucky ground for the Indian team as they have not lost a Test match at this venue for the last 22 years.
They lost the first Test to be hosted in this stadium in 1994 against the West Indies. It was their last Test defeat at this ground and since then, India have won six Tests and drawn five here.
It certainly seemed that the Indians will continue that long unbeaten record in the morning session when riding on a disciplined bowling effort, the hosts reduced England to 92/4 by lunch.
Electing to bat after winning the toss, England lost opener Haseeb Hameed (9) before skipper Alastair Cook (27) and Joe Root (15) took them past the 50-run mark.
But the hosts quickly turned it around with three quick wickets of Cook, Root and Moeen Ali (16) just before the lunch break to put the visitors on the backfoot.
Stumper Jonny Bairstow (20) and Ben Stokes (5) were at the crease when the umpires called for lunch.
Teenaged opener Hameed, who survived 31 balls, was the first casualty for the English side when a short of a good length delivery from pacer Umesh Yadav hit his gloves to give an easy catch to Ajinkya Rahane at gully.
Root then joined Cook in the middle but failed to impress before succumbing leg before to off-spinner Jayant Yadav as the visitors were reduced to 51/2.
Cook, meanwhile failed to capitalise on the two dropped chances -- dropped on 4 by Ravindra Jadeja and then on 23 by Ravichandran Ashwin -- both off pacer Mohammed Shami.
His 42-ball vigil at the crease was cut short by a short and wide delivery from Ashwin, which resulted in a thin edge for stumper Parthiv Patel. Cook batted fluently for his 27, which was laced with six hits to the fence.
Tottering at 51/3, India skipper Virat Kohli immediately brought back Shami into the attack which the Bengal pacer responded beautifully by packing left-hander Moeen Ali.
Back for his second spell, Shami induced Ali with a short delivery, which resulted in a top edge only to be caught at fine leg by Murali Vijay.
Ali looked confident in the middle hitting Jayant Yadav for a consecutive four and a six during his 45-ball stay. Thereafter, Bairstow and Stokes survived a few anxious moments to take England to 92/4 when the umpires signalled for the lunch break.
For India, all the bowlers -- Umesh, Shami, Jayant and Ashwin managed to take a wicket each while Jadeja was yet to be introduced into the attack in the morning session.
Bairstow and Stokes batted steadily after lunch as they calmly went about accumulating the runs.
Stokes scored 29 runs off 59 balls with five hits to the fence before being stumped off Jadeja's bowling.
Jadeja, who was quite poor in the field during the morning session, including a dropped chance off Cook in the slips, made amends when he got one to spin sharply in.
Stokes, who had attempted a drive, was surprised by Jadeja's pace as the ball beat the outer edge on its way to wicketkeeper Parthiv Patel who whipped off the bails.
Bairstow and Stokes had added 57 runs between them.
Stokes' departure saw Jos Buttler join Bairstow in the middle and the duo proceeded to try and salvage the England innings.
England (First Innings): 205/5 (Jonny Bairstow 66 batting, Jos Buttler 38 batting) vs India.
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