Resuming day 3 on 154/1, Smriti Mandhana feel for 70, while Yastika Bhatia (113) hit the first-ever Women's Test ton at Lord's.
Bhatia's 161-run stand with Mandhana laid the platform before Richa Ghosh's 50* took India to 341/7 declared.
Sophie Ecclestone starred with 5/118, but India set England a massive 457-run target.
England's chase began disastrously as Tammy Beaumont and Maia Bouchier feel cheaply, leaving the hosts at 6/2.
Heather Knight's too walked back early in her final international innings, while Sayali Satghare and Sneh Rana reduced England to 59/5.
Amy Jones fought back with a 52*, but Rana broke the resistance as Richa Ghosh pulled off a stunning catch behind the stumps.
At stumps, England were 130/6, still needing 327 runs, while India stands just four wickets away from a famous Test win at Lord's.