The series will now be decided in the final match in Hamilton on Sunday.
New Zealand won the series opener by six runs in Auckland on Monday and a follow-up victory would see them regain the Chappell-Hadlee Trophy they lost in a 3-0 whitewash in Australia in early December.
The rain eased off in Napier around the time of the scheduled 2:00pm start and the umpires at one stage announced a new time with the game reduced to 37 overs.