The tourists had declared on 352-7 on day three to leave England needing 498 over the final two days for victory, and a 169-run partnership between Ben Stokes and Jos Buttler ensured that their efforts will go until the last day at Trent Bridge.
However, the hosts still need 210 runs on the final day, while India need only one more wicket after England ended day four on 311-9.
Buttler was the main protagonist in England's stubborn performance as he produced his maiden Test century, striking up a timely partnership with Stokes (62).
However, Buttler was eventually bowled for 106 by India's Jasprit Bumrah, who did the main damage on the day with a five-wicket haul - also claiming the scalps of Joe Root (13), Jonny Bairstow (0), Chris Woakes (4) and Stuart Broad (20) to tear through the middle order and tail.
However, barring unexpected bad weather India are likely to wrap up the victory with minimum fuss on day five, which would see them pull the five-match series back to 2-1.