India were set a target of 245 to win the fourth Test against England on the fourth day of five at Southampton on Sunday.
England, 2-1 up in this five-match series, were eventually dismissed for 271 in their second innings after resuming on their overnight 260 for eight.
Mohammed Shami struck with the first ball of the day's play to have Stuart Broad caught behind for a golden duck.
That left Shami, for the second time in the match, on a hat-trick at the start of his next over after he had removed Adil Rashid with the last ball of Saturday's play.
Sam Curran, 37 not out overnight, survived the hat-trick.
But in sight of his second fifty of the match, Curran was run out for 46 going for a second by Ishant Sharma's throw to wicket-keeper Rishabh Pant.
Pace bowler Shami led India's attack with four wickets for 57 runs from 16 overs.
India have scored 200 or more to win in the fourth innings of a Test outside of Asia just three times -- 406 for four against the West Indies at Port-of-Spain in 1975/76, 233 for six against Australia in Adelaide in 2003/04 and 200 for five against New Zealand at Dunedin 1967/68.
They are now bidding to become just the second side in history to win a five-match Test series from 2-0 down, with an Australia side inspired by batting great Don Bradman the only team to have achieved the feat, against England in 1936/37.