India made 521-8 declared batting first, before bowling England out for 191 to enforce the follow-on to try and wrap up the victory without having to bat again.
England captain Alastair Cook scored 176 and Matt Prior made 91 as the tourists took the match into a fifth day.
England started the final day on 340-5, 10 runs ahead of the hosts, but they lost Cook and Prior in the first hour.
“It was a great fightback, we were in a really tough situation,” said Cook, playing his first match as England Test captain since being appointed. “To get it to the last day, there’s always a glimmer of hope with five down and it had to be something very special. Unfortunately, it wasn’t to be today, but we fought hard and we can take a lot from the second half of this game with our batting.”