Having scored 141 runs in the afternoon session to take the lead past 100, England continued to dominant after tea, with Bairstow reaching his half-century and Woakes following suit shortly after.
For much of the day, thanks again to the weather, it looked as though the fans were going to be restricted to just over eight overs of cricket but then the weather cleared in the evening and India must have wished the rain had stuck around.
"It´s an incredible feeling to raise your bat at Lord´s and be on that honours board", he added.
And welcome to our live blog of day four of the Lord's Test match.
The 29-year-old Woakes is playing in place of Ben Stokes, who was forced to miss the second test as he stands trial in a court in Bristol charged with affray.
Pujara and Kohli were involved in a run out which led to Pujara's wicket and turned the match in England's favour.
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Chris Woakes celebrates his first Test century, the all-rounder ended the day on 120 not out. "And Woakes and Bairstow took the game away".
The 20-year-old Ollie Pope impressed on debut but fell for 28 before captain Joe Root, strangely subdued, was lbw to Shami for 19 with the last ball before lunch.
Unfortunately for the tourists Buttler got 24 off 35 balls - quick scoring on this wicket - before he was LBW off Shami (three for 67).
Earlier, India made a decision to play with two spinners in Ravichandran Ashwin and Kuldeep Yadav, whereas Cheteshwar Pujara had a horrific return to Test cricket.
Saturday´s play resumed with England yet to begin their reply after James Anderson, in overcast conditions ideal for swing bowling, had taken five for 20 on Friday following Thursday´s total washout.
"It would've been nice to have had a little bit more red-ball cricket under my belt (before the Test) but I definitely felt I was ready from the mental side of things if called upon". As so often happens they did not have to wait long fir the second wicket, Alastair Cook caught behind for 21 off Ishant Sharma (one for 26) to leave England on 32 for two.