The Delhi-born cricketer is presently playing the second Test of India's tour of England at Lord's. Bairstow was 62 not out and recalled all-rounder Woakes 55 not out.
Virat Kohli was trapped in an almighty mix-up as the Indian captain's blunder led to Cheteshwar Pujara being run out as India were skittled for 107 by England on day two of the second test at Lord's on Friday (Saturday NZ time).
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.
Credit for the latter should at least partially be assigned to Woakes, he defended well, played strongly on the drive through the offside and looked more than a match for anything India had to offer - as if mild-mannerly showing the world that the nine first class centuries he has for Warwickshire were not acquired by accident.
Kohli had single-handedly made the first test at Edgbaston competitive, his 200 runs failing to save India as England took a 1-0 lead in the five-match series, but he couldn't repeat his heroics on a green wicket at Lord's.
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Anderson's new ball partner Stuart Broad then joined the party with the wicket of Ashwin, who looked good during his 38-ball stay, that also included four fearless hits to the fence.
The exit of England's all-time leading Test run-scorer meant 20-year-old debutant batsman Ollie Pope walked out with the hosts in trouble at 32 for two.
And to what became the last ball before lunch, Root was lbw for 19 to a off-cutter that kept low, with Bairstow then unbeaten on four.
Even though Bairstow was the more senior of the pair, it was Woakes who looked the more impressive, driving, cutting and pulling the ball with authority around the Lord's outfield. Five balls later, Ishant came up with a beauty to put his indifferent start behind him as Cook (21) edged one behind to the 'keeper. With the partnership appearing to take the game away from India, Hardik struck at a vital juncture in the game trapping Pope (28) plumb in front.
Woakes' top Test score was 66 before this innings but he soon reached his first century for England off just 129 balls in an innings which included 15 boundaries.