India, who had upset seventh seeds Ireland in their tournament opener before clinching pole position in Pool G, are taking part in the biennial tournament for the third time only.
They had finished 18th in their debut in 2002 and 11th last year.
Anaka Alankamony, the number three in the squad, gave 10th seeds India the lead with a resounding 3-0 (11-8, 11-6, 11-5) win over Milou van der Heij but it was even-steven with Indian number one Dipika Pallikal losing 8-11, 4-11, 3-11 to Natalie Grinham in the second game of the Round of 16 tie.
World number 13 Pallikal was outplayed by her stronger rival Natalie, who is currently ranked 11 in the world.
It was left to Joshana Chinappa to show that the top-spot finish in the pool was no fluke and she beat Orla Noom in a tense deciding game 5-11, 11-9, 8-1, 11-2, 11-3.
Earlier, India had thrashed Argentina 3-0 to clinch pole position in Pool G.
The event boasts of a record entry of 26 nations and is being staged simultaneously at both the eight-court Club des Costieres and La Parnasse Arena where, for the first time ever, action is taking place on three all-glass show courts.
Result:
Round of 16: (10) India bt (8) The Netherlands 2-1
Anaka Alankamony bt Milou van der Heij 11-8, 11-6, 11-5; Natalie Grinham bt Dipika Pallikal 11-8, 11-4, 11-3; Joshana Chinappa bt Orla Noom 5-11, 11-9, 8-1, 11-2, 11-3.
