New Zealand went into the game on the back of an impressive 58-run upset win over India in their opening game.
However, the defending champions controlled the tempo throughout the game in Sharjah.
Australia got off to a strong start with Alyssa Healy, Beth Mooney, Ellyse Perry and Phoebe Litchfield all scoring at better than a run a ball.
Mooney top-scored with 40, while Perry made 30 as Australia finished on 148 for eight.
New Zealand did manage to peg back the Australian lower order with spinner Amelia Kerr taking four wickets and two each for Rosemary Mair and Brooke Halliday.
New Zealand made a good start in reply. Suzie Bates scored 20 and Kerr 29, but they slumped from 54 for one to 60 for six as they tried to lift the run-rate.
The White Ferns then limped through the rest of the game before being bowled for 88 in the last over.
Australian medium pacer Megan Schutt finished with three wickets for three runs, while Annabel Sutherland also took three wickets.
White Ferns captain Sophie Devine gave an honest appraisal in the after-match interviews.
"We needed a good start and probably let the run rate creep up too much.
"Disappointing night for us but we said after the first game that we're not going to get too high and equally we're not going to get as low with this game."
It was Australia's 13th win in a row in T20 World Cups and takes them top of Group A.
New Zealand drop to third in their group behind Pakistan who also have one win from two games but at a better run-rate than New Zealand.
Devine felt her side could improve in all three facets of the game.
"I thought with the ball we strayed too much from the stumps, in the field we were a bit sloppy and with the bat we need to be a bit more courageous."
Despite the loss New Zealand is still well-placed to qualify for the semifinals following their first-up win over India.
Wins against Sri Lanka and Pakistan in their next two games should be enough unless there are some other upsets and the equation comes down to run rate.
"We need to win, we don't want to look too far ahead, so Sri Lanka is now our most important game of this tournament," Devine said.
That game against Sri Lanka is on Saturday night New Zealand time.
