They also made light work of their chase. India's openers Punam Raut (69) and Thirush Kamini (43) put on 119 for the first wicket - Raut was dropped at first slip in the first over - before captain Mithali Raj (36 not out) and Harmanpreet Kaur (46 not out) guided their side to an easy win.
In a change to the original World Cup schedule, the White Ferns will now play all of their pool matches in Cuttack rather than Mumbai.
A series of non-violent demonstrations around Pakistan's involvement in the tournament, mainly in Mumbai, has seen the ICC and BCCI take the precautionary measure of shifting all Group B fixtures, plus some super-six and playoff matches, to Cuttack on the east coast of India.
If they advance from the group stages, the White Ferns will play all of their super-six matches in Mumbai.
New Zealand 201 in 47.5 overs (Suzie Bates 27, Sara McGlashan 56, Frances MacKay 69; Jhulan Goswami 3-26, Ekta Bisht 2-32, Gouher Sultana 2-35) lost to India 204/2 in 43.3 overs (Poonam Raut 69, Thirush Kamini 43, Mithali Raj 36*, Harmanpreet Kaur 46*) by 8 wickets.