England were set an implausible 478 to win and were all out in 27.3 overs.
Deepti Sharma finished with nine wickets after taking 4-32, and Pooja Vastrakar impressed with 3-23.
India has defeated England in a home Test for the first time.
Before the start of play, India captain Harmanpreet Kaur declared on 186-6, setting England the highest-ever chase in women’s Test cricket, or the unusual challenge of batting the next two days for a draw.