England captain Alastair Cook called a halt when he himself was 70 not out after Joe Root (56) was bowled by left-arm spinner Ravindra Jadeja (three for 52).
Cook and Root added 99 in just 87 balls as England pressed for their first win in 11 Tests.
The most any side has made in the fourth innings to win a Test is the 418 for seven West Indies achieved against Australia at St John's in 2002/03.
India's highest total in the fourth innings to win a Test is 406 for four against the West Indies at Port of Spain in 1975/76, with their next best winning chase the 287 for four they posted against England at Chennai in 2008.
India lead this current five-match series with England 1-0 after their 95-run win in the second Test at Lord's.