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As an Indian national and holding a valid New Zealand Visa , you are eligible to transit in Singapore airport for one transit (96 Hours) provided you have valid ticket and visa for onward journey to one of the following countries:
Answer is from official immigration and checkpoint authority Singapore Source : https://www.ica.gov.sg/page.aspx?pageid=96
Visa Free Transit Facility (VFTF)
General Conditions:
Transit travellers who satisfy the criteria for VFTF will have to meet the prevailing entry requirements before they are allowed entry into Singapore. Assessment for entry is determined by the Immigration & Checkpoints Authority (ICA) officers at the point of entry.
Extension of stay for transit travellers under the VFTF is strictly not allowed
You don't need a Singapore visa for this itinerary, simply you can avail transit visa at Singapore immigration in Changi Airport