Their unbroken sixth-wicket stand was so far worth 99 runs and all the more valuable for the fact that England had slumped to 89 for four on the stroke of lunch.
Bairstow slowed down with the landmark in sight and paid the price for it with Hardik Pandya (2/66) nabbing him just short of three-figures. Woakes got to the century before Hardik Pandya removed a exhausted Bairstow for 93 (144 b, 12x4), Dinesh Karthik taking a diving catch to his right.
Bairstow came to the crease when England were in a spot of bother. India took the second new ball as soon as it was due, but the players went off for bad light after just one over.More news: Hurricane Hector to pass just south of Hawaii
Virat Kohli's mistake led to Cheteshwar Pujara being run out. In a quest for a desperate breakthrough, India wasted a review. With a lot of cloud cover, India still had hopes of a comeback in the match at that point. He later missed the third and final T20I of the series citing a sore back.
After rain meant there was no play on Thursday, Anderson struck with the fifth ball of the match when Murali Vijay, aiming legside, was undone by late outswing and bowled for a duck. The duo started the third session in the same manner as Woakes reached his century off 129 balls. They took the score past the 200-run mark and the lead beyond 100.
That easy wicket for England left India at 3/15.
This second day may have begun in bright sunshine. They took a couple of overs to find the proper line and length to bowl at the two left-handed opening batsmen.More news: Samsung Galaxy Note 9 forums are now open
It became a double blow as five balls later Alastair Cook (21) was caught behind off Sharma and the hosts were reduced to 32/2.
England captain Joe Root confirmed on Wednesday that Ollie Pope, a 20-year-old Surrey batsman, would make his Test debut in place of the dropped Dawid Malan. It was an lbw, there was no inside edge in the pad, but England's DRS seems to have gone waste.
Rahane's patience gave away as Amderson coming for his second spell bowled a beauty to force him to edging one to the slips as India's resistance ended in a jiffy.More news: Trump doubles tariffs on Turkey, stoking jitters