Woakes took three wickets during a productive morning spell that gave England the upper hand.
After the batting debacle in the first two Tests of the ongoing five-match series between India and England, visitors put up their best batting performance on Saturday by reaching 307 for 6 on the first day of the third Test.
England - 2-0 up and aiming to seal a series victory - looked set to have their decision to field first vindicated as the ball moved around on a grassy surface.
As well as India competed in the thrilling first Test at Edgbaston, their capitulation in the second at Lord's raised fears the remainder of the series would be one-sided. However, Vijay seemed particularly unlucky to have lost his place at the top of the order, having been dismissed by two unplayable balls in the second Test.
For the 45th consecutive Test, they tinkered with their team - including fit-again pace bowler Jasprit Bumrah, giving a debut to 20-year-old wicketkeeper Rishabh Pant and recalling opener Shikhar Dhawan.
There a moment of concern for England shortly after tea when Stuart Broad, taking his mark at the Radcliffe Road End, was stung on the lip by a wasp.
"I think the first day's total is quite decent". The duo always kept the scoreboard ticking despite the England bowlers maintaining a good channel.
On his way to 97, Kohli became the highest scoring Indian captain in away Tests.
There was still time for a catch to go down as Keaton Jennings spilled Hardik Pandya at third slip after the hosts had taken the new ball but Jos Buttler made no mistake as he got rid of the all-rounder with the final ball of the day for 18.
After Joe Root had sent India in to bat, England's captain needed his four seam bowlers to pitch a full length, but Stokes bowled too short in his zeal to make an immediate impression on his return. But credit to India, I thought they played pretty well.
Ravichandran Ashwin fell for 14 when Broad, on his Nottinghamshire home ground, uprooted the middle stump as the batsman aimed legside.
"I'm really looking forward to seeing how the England batsmen play when the opposition has a good score on the board".