Despite India"s 207 runs in 49.4 overs, the 78-run opening partnership between Pulford and Haidee Tiffen put Kiwis on course for victory.
Anjum Chopra (52) and Mithali Raj (21) pulled India out of trouble and managed to get over-200 score for the second time in the tournament.
Chopra and Raj put on 36 runs but only at the rate of three runs per over. It was left to the lower order to provide some push and Reema Malhotra did just that with a quickfire maiden half-century.
She remained unbeaten on 59, got good support from the tail, adding 27 at more than five an over with Amita Sharma (14 off 16) and 44 at more than nine an over with Harmanpreet Kaur (13 off 16).
However, the New Zealand medium-pacers, Nicola Browne and Bates, bowled accurately to ensure that India didn"t get away with a big score.
The target of 208 was competitive but Kate Pulford set up the chase with an 89-ball 71 and a nerveless Suzie Bates (47 not out) saw them through after the Indian spinners got some quick wickets.
India are ahead of New Zealand on net run-rate and can still reach the final, but only if they beat West Indies, New Zealand go down to Pakistan and Australia lose to England.