David picked four for 48 to restrict the English women to a modest 188 but the hosts suffered a middle order collapse and ended up with 168 for nine at the Nahar Singh stadium.
England lead the five-match series 1-0 with the second tie to be held in Lucknow [ Images ] on Dec 1.
Harper returned with 4-33 as India, needing 35 runs in the last four overs with seven wickets in hand, lost six wickets for only 15 runs in the closing stages.
Visiting captain Charlotte Edwards was named player of the match for her 122-ball 68 punctuated with six fours that laid the foundation for England's total.
Jenny Gunn was the other notable contributor with 56 from 101 balls and she added 90 runs for the third wicket with her captain.
India began well with Monica Sumra (59) providing a solid start in the company of Jaya Sharma (18) as the two put on 68 runs for the opening stand.
Anjum Chopra [ Images ] (33) then joined Sumra for a crucial second wicket partnership before the latter fell leg before to Rosalie Birch.