The defending champions are now the only unbeaten team in Group A and can all-but secure their passage by beating Pakistan in Dubai on Friday (Saturday 0100 AEDT).
Australia were ultimately disappointed with posting 8-148, but it was ample 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. But the middle and lower order folded.
Beth Mooney top-scored for Australia with 40 as they posted 8-148 against New Zealand in Sharjah. (AP PHOTO)
"We could have been smarter with the bat at the end, but we came out really well with the ball and I'm really happy with that," said skipper Alyssa Healy.
"Megan Schutt has been wonderful, but I thought the whole attack tonight was unbelievable."
As against Sri Lanka Schutt set the tone 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 last 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 a 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.
Megan Schutt picked up three wickets to become the sole highest Women's T20 World Cup wicket-taker. (AP PHOTO)
"When we were bowling we strayed a little too far from the stumps," Devine said. "In the field we were a little sloppy. With the bat we need to play some more courageous shots. We needed to have a good start and we let the run rate creep up too much."
Australia, who switched in Grace Harris for Darcie Brown, won the toss and elected to bat. Healy, having survived two early reviews, cracked two fours in the third over and her team were up-and-running. After 31 balls they were 0-41.
But a series of batters got in, and got out. Healy skied Rosemary Mair for 26 off 20 balls, Mooney was caught at mid-off and Ellyse Perry, having been dropped on four, misread 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 her brilliant catch 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 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.
Yet 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 and proved more than enough.
