The defending champions are now the only unbeaten team in Group A and can all-but secure their passage with victory against Pakistan in Dubai on Friday.
Australia were ultimately disappointed with posting 8-148, but it was more than enough against a New Zealand side they have now beaten ten times in succession.
Having been 1-79 at the halfway mark Australia scored 69 runs for the loss of seven wickets in the second ten overs. Beth Mooney top-scored, following up her 43 in the opening win over Sri Lanka with a 32-ball 40.
Beth Mooney top-scored for Australia with 40 as they posted 8-148 against New Zealand in Sharjah. (AP PHOTO)
As against Sri Lanka Megan Schutt set the tone with the ball taking a wicket in the third over, bowling Georgia Plimmer (4). That made her the sole record holder for most wickets in T20 World Cups with 44.
She returned midway through the innings to claim her 45th, the dangerous Amelia Kerr (29 off 31), then finished the match in the final over to end the innings with 3-3 off 20 balls and 6-15 in the tournament so far.
When Kerr went the Kiwis were already chasing ten an over, a near-impossibility against Australia's attack on this slow, used track. Sophie Molineux (2-15) had just accounted for Suzie Bates (20 off 27) and a repeat of skipper Sophie Devine's 36-ball unbeaten 57 in their boilover win against India was New Zealand's last hope.
But she never got going as wickets fell at the other end including two in two balls for Annabel Sutherland (3-21). The Kiwis' last nine wickets fell for 34 runs with Devine ninth out after making seven off 15 balls.
Megan Schutt picked up three wickets to become the sole highest Women's T20 World Cup wicket-taker. (AP PHOTO)
Australia, who switched in Grace Harris for Darcie Brown, won the toss and elected to bat first. Two balls in New Zealand burned a review when a ball from Rosemary Mair brushed Alyssa Healy's pad on its way down the leg side with the bat nowhere near.
Twelve balls later it was Healy, on four, reviewing after being given out leg before to Fran Jones attempting a reverse sweep with the score on nine. The ball was hitting, but impact was outside off stump and the skipper, reprieved, took advantage with ten off the next three balls.
From there Australia were up-and-running. After 31 balls they were 0-41. But a series of batters got in, then got out.
Healy skied Mair for 26 off 20 balls, Mooney was caught at mid-off and Ellyse Perry, having been dropped on four, misjudged Amelia Kerr's googly to be bowled for 30 off 24 balls.
Kerr followed up by bowling Harris the same way next ball, putting a smile back on her face after what appeared a brilliant catch by her to dismiss Phoebe Litchfield for one was controversially judged to have been grounded on TV replay.
Thereafter Australia, seeking rapid runs, lost wickets quickly. The much-vaunted middle-order is chock-full of all-rounders but none reached double figures as Kerr (4-26), Brooke Halliday (2-16) and Mair (2-22) chipped away.
Nevertheless, while the score may not have been the 160-170 that at one stage looked likely, it was the highest of the six matches played so far at Sharjah.
New Zealand, against India in Dubai, are the only team in ten matches to have scored more but they never looked like coming close to a repeat.
