India's lower-order, led by Ravindra Jadeja, put up some magnificent resistance to nullify the home side's bowling attack and came close to pulling off an epic win at the Home of Cricket.
The tourists came into the final day on 55-4, still 138 short of chasing down the 193-run target, but all the planning went array in the first session as they lost four wickets.
Rishabh Pant was bowled by a fired-up Jofra Archer before home captain Ben Stokes trapped overnight batter KL Rahul lbw for 39.
It was 82-7 when Archer took a brilliant one-handed catch to dismiss Washington Sundar while Nitish Reddy was caught behind off Chris Woakes to leave India 112-8 at the lunch interval.
It looked as though the Test would be done quickly after the break but Jasprit Bumrah survived 54 balls, and 104 minutes, in a partnership with Jadeja that yielded 35 runs.
Stokes then made the breakthrough with the total on 147 as Bumrah's resistance came to an end, a swing with bat by the tail-ender saw him caught at deep mid-on.
Mohammed Siraj then kept Jadeja company and the all-rounder reached his second fifty of the Test, to go with his 72 in the first innings, as India inched ever closer to the target.
However, not long after tea, spinner Shoaib Bashir bowled Siraj with the batter unlucky as he blocked a ball that trickled back onto his stumps to spark wild celebrations from the home side and Jadeja left stranded on 61.
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