New Zealand were undone by offspinner Shane Shillingford, who took all four wickets as the hosts' got fidgety as they eyed their first win in 10 tests, only to run out of time.
The rain was always expected to arrive but New Zealand couldn't get going in their second innings.
Ross Taylor, the first innings double centurymaker, spent 94 minutes over 16 not out, while Corey Anderson was on 20 when the rain came.
Shillingford finished with four for 26 off 15 tight and penetrative overs.
New Zealand's last test victory was in Colombo last November. Since then they have lost four tests - two each against South Africa and England - and drawn five, three against England and two against Bangladesh.
The second test starts in Wellington next Wednesday.
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