The rain washed out the one chance the West Indies had to make amends for a dismal tour, after they were beaten 1-4 in the earlier One-day series.
But although they made their best start of the tour, reaching 256 for four in the rain-disrupted first two days, they could go no further with the remaining three days all washed out.
The abrupt end left a frustrated Runako Morton unbeaten on 70, his second half-century in consecutive Tests, and eyeing consecutive centuries at McLean Park here after his 110 not out in the fourth One-dayer last month.
Morton is in a select group of West Indies batsmen who can leave New Zealand with their reputation enhanced.
Brian Lara produced a drought-breaking 83 here, his first score in double figures from five innings on tour.
The draw snaps an eight-Test losing streak for the West Indies who head home to prepare for a seven-match One-day series against Zimbabwe before hosting India for five One-dayers and four Tests.
New Zealand take heart from a series win, and the second Test victory gave them five wins in succession for the first time in the nation's cricketing history.
An added bonus for New Zealand has been the rain, which has allowed their bowlers to take a breather before embarking on what should be a much tougher Test series in South Africa.
The touring party includes the 13 players in the squad that crushed the West Indies plus the recall of allrounder Jacob Oram and opening batsman Michael Papps.
New Zealand coach and convenor of selectors John Bracewell said he was not too perturbed with their final dress rehearsal for South Africa being washed out.
If anything, the abbreviated match allowed his slightly weary pace attack some valuable recuperation time after bowling the West Indies out four times in the first two Tests.
Bracewell conceded at the squad announcement that some of his bowlers were just "hanging on", but the weather-enforced break had allowed some low batteries to be recharged before their warm-up match against the Rest of South Africa XI starting on April 7.
"It was likely that we probably would not have played Shane Bond, James Franklin and Chris Martin (against the Rest of South Africa) and just warmed them up in the nets and acclimatise them.
"Now we have to rethink that because they are a lot fresher then we expected them to be at the end of the season," Bracewell said.