Ben Duckett smashed a superb hundred while Joe Root hit an unbeaten half-century as England chased a massive 371-run target at Headingley on Tuesday.
Joe Root finished with 53 not out with wicketkeeper Jamie Smith unbeaten on 44 as England complete the record run-chase with five wickets to spare. This was England's second highest chase against India.
Krishna, in only his fourth Test, struck twice in quick succession to leave England 206-2 following a superb opening stand of 188 between Duckett and Zak Crawley (65).
And medium-pacer Thakur then took two wickets in two balls as Harry Brook followed the prize scalp of Duckett for 149, to leave England 253-4.
Play had continued through fine drizzle in the morning session as Duckett and Crawley withstood a stern test from star paceman Jasprit Bumrah and Mohammed Siraj.
But after a 20-minute stoppage for rain, India finally broke through thanks to the inexperienced Krishna, who had 2-69 in 11 overs at tea.
One ball after pulling Krishna for four, Crawley edged a drive to first slip, where KL Rahul held a sharp catch.
Crawley's exit brought in Ollie Pope after the vice-captain top-scored with 106 in England's first-innings 465.
Pope, however, could only manage eight before he was bowled by a fine ball from Krishna that nipped back.
Duckett dropped
An undaunted Duckett continued his assault with a reverse sweep off Ravindra Jadeja for an extraordinary six.
But his impressive innings ended when he drove Thakur to short extra cover where substitute fielder Nitish Kumar Reddy, in a game of dropped chances, clung on to a sharp catch.
Next ball Harry Brook, out for 99 in England's first innings, saw a whip shot well caught down the legside by wicketkeeper Rishabh Pant.
Stokes survived the hat-trick but the game is back in the balance.
Earlier, Duckett was fortunate to complete his sixth hundred in 34 Tests.
He had made 97 when he top-edged a pull off Siraj only for Yashasvi Jaiswal, running in from deep square leg, to drop the catch to the fast bowler's visible fury.
If England achieve their target, it will be just behind their record fourth-innings chase of 378 against India at Edgbaston three years ago.
It would also be the second-highest chase in a Test at Headingley, surpassing England's 362-9 against Australia in 2019 when Stokes' unbeaten century secured a stunning one-wicket Ashes win.
England resumed on 21-0, with both sides eyeing an early lead in the five-match series.
Crawley (12 not out) and Duckett (nine not out) were confronted with the daunting task of facing Bumrah, fresh from a five-wicket haul in the first innings, in overcast conditions.
Duckett went on the attack after lunch, on-driving Bumrah for a superb four, before a quick single took Crawley to a 111-ball fifty — the slowest of his England career but still hugely valuable.
Pant became only the second wicketkeeper to score two hundreds in a Test when he made 118 on Sunday to follow his first-innings 134.
But, despite five individual centuries in this match, India would have been in a stronger position had they not suffered collapses of 7-41 and 6-31 at the back end of each innings.
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