New Zealand will face either South Africa or India in their first Super Eight match at Barbados on Friday morning (NZT) after barely raising a sweat at Providence Stadium.
McCullum earned his second straight man-of-the-match award by taking three for 16 at the top of the innings as Zimbabwe were skittled for 84 in the 16th over -- the 12th-lowest total in Twenty20 international history.
New Zealand cruised to 36 for one in the ninth over before rain began to fell. The teams returned to the outfield an hour later but play was abandoned and the result was determined under the Duckworth-Lewis method.
Zimbabwe, who were eliminated from the tournament, made a bright start to be 58 for one in the seventh over before opener Hamilton Masakadza was run out for 20 courtesy of sharp work in the deep from Jacob Oram, sparking a collapse.
New ball exponent McCullum claimed three key scalps in one over -- the ninth -- with his off spin.
He had the dangerous Elton Chigumbura caught at long-on for three off the first ball. Charles Coventry was out for nought after offering a simple caught and bowled chance and off off the over's last ball Craig Ervine (one) was stumped by wicketkeeper Gareth Hopkins.
Medium pacer Scott Styris then chimed in with three for five in two overs to effectively seal the result.
"We fought back well in the middle stages with Nathan and Scott Styris," said captain Daniel Vettori, who won the toss and took two for 10 himself.
"We knew it would be a difficult track to bat with Zimbabwe having so many spinners and we did well to come back in the middle overs."
Opener Tatenda Taibu top-scored with 21, a score that was pipped by New Zealand counterpart Brendon McCullum's unbeaten 22 off 26 balls, which included two fours. In the process, McCullum became the first player to bring up 1000 Twenty20 international runs.
Jesse Ryder fell for two and Martin Guptill was on six when the rain arrived.
Zimbabwe came into the tournament as one of the form teams after shocking Pakistan and Australia in the warm-ups but they struggled against Sri Lanka and Zimbabwe.
"It is disappointing," said captain Prosper Utseya.
"We had a good start but we didn't play well in the middle. There is potential no doubt. But some guys have to mature as cricketers."
New Zealand, who pipped Sri Lanka by two wickets on Saturday, qualify top from group B.
Their second Super Eight opponents on Sunday will be Pakistan in Barbados, following by England at St Lucia on Tuesday next week.
Nathan McCullum expected a change in approach would be needed for those matches.
"It's going to be different wickets further up in the country, hopefully we can continue to do well," he said.
