A 195-run partnership between KL Rahul (137) and Rishabh Pant (118) had put India in control before Josh Tongue swung momentum back by seeing off the Indian tail, three wickets in four balls helping ensure the tourists lost their final six second-innings wickets for 31 runs.
The collapse, which had India all out for 364, gave the dangerous Jasprit Bumrah the chance to attack England before close of play, but neither Zak Crawley nor Ben Duckett looked troubled.
Asked if sharing the spoils in this series opener would be acceptable, Tongue said: "No. I think we'll just go for the win.
"That's the clear message in the changing room. It's just being as positive as we can. They're going to bowl well at times, so it's just crucial we soak up that bit of pressure and reapply it again on their bowlers.
"I don't see why we can't chase that down. With our batting line-up I feel we can chase anything down."
Tongue also saw fit to raise memories of Stokes' finest hour as a Test cricketer, his 'miracle of Headingley' in 2019, where a magical century carried England to 359 by a solitary wicket.
"I remember Stokesy's innings here against the Aussies," he added with a smile.
England have only drawn one from 35 Tests under the current regime, with one of their exhilarating run chases in that spell coming when they reached 378 against India in 2022 -- the only time India have lost when defending a Test total of more than 350.
Resuming day four on 2-90 in their second innings, with a lead of 96 runs, India captain Shubman Gill chopped onto his stumps to fall for eight, a second wicket for Brydon Carse.
But Rahul and Pant looked set to put the game beyond England. Rahul's century was his ninth in tests, eight of which have come overseas, while Pant's made him the second wicket-keeper batsman, after Zimbabwe's Andy Flower, to score a century in each innings of a Test.
Pant eventually tried one shot too many, caught chasing another six on the boundary before Rahul chopped onto the stumps off the bowling of Carse.
Then came the Tongue-inspired collapse as the touring side, having lost their final six first-innings wickets for 24 runs, fell apart again.
"Someone's got to win tomorrow, it will be an interesting day," Rahul said.
"The wicket is not as easy as the first innings, they won't find it as easy to hit the ball on the rise. Even if they get a big partnership, if we get a couple of wickets we'll be right in the game."
