Woakes scored an unbeaten 120 in tricky conditions as England batted through a slightly abbreviated day to finish at 357 for six, while Jonny Bairstow contributed 93 to a record sixth-wicket partnership of 199 for England against India.
But while the Yorkshireman deserved to reach three figures, his despair will surely be tempered by the sight of Woakes reaching his first Test century at the home of cricket, becoming only the seventh Englishman to be on both honors boards at Lord's.
For the tourists it seems their only hope of avoiding defeat and going 2-0 down in the five-match series is to perform a rain dance and hope the heavens open.
Kohli, who was looking all at sea against Woakes, finally fell to the right-armer in his third over, with Jos Buttler making no mistake this time at second slip.
On the stroke of lunch, the impressive Shami picked up his second wicket with a ball that kept low and cannoned into Root's pads.
India had recalled left-arm wrist-spinner Kuldeep Yadav, who tormented England during the preceding one-day series, for just his third Test after dropping paceman Umesh Yadav, who bowled well at Edgbaston.
With the forecast set fair for Saturday, it will be the turn of England's batsmen to drive home the advantage given to them by their bowlers on a day where there were two stoppages for rain spanning more than five hours.
Shami changed the angle after not finding success initially and the move paid off immediately with Keaton Jennings (11) getting trapped plumb in front off a full delivery. 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.
But a promising innings of 28 ended when Pope was lbw to all-rounder Hardik Pandya.
After the entire first day was lost to rain, further wet conditions forced a delayed start with England captain Joe Root eventually winning the toss and putting India in to bat on Friday. The Indian batsmen have themselves to blame as much as the top-class bowling from the English fast-bowlers led by James Anderson.