The victory has put the White Ferns in the prime spot to qualify top of their group with one game left in their pool match.
The victory by six wickets was set up by an impressive bowling performance from the White Ferns, with spin to the fore.
The match was played on the same wicket in Nagpur on which the Black Caps beat India last week and Kasperek and Nielsen bowled eight overs between them up front after Australia had won the toss and elected to bat on the same pitch.
The experienced Nielsen exerted her influence at the other end to finish her four overs having conceded just four runs, before legspinner Erin Bermingham took over in an innings in which all but five of the 20 overs bowled by a four-prong spin attack.
Sophie Devine's injection of pace proved successful as she picked up her 50th T20 international wicket, trapping a fighting Ellyse Perry on 42 to achieve the 50 wickets-1000 runs double.
The wicket halted a 50-run stand and a significant recovery from Perry and Jess Jonassen. Devine then also took a spectacular diving catch to dismiss Megan Schutt off spinner Amy Satterthwaite as the New Zealanders restricted Australia to its lowest T20 total of 103 for eight wickets.
Openers Suzie Bates and Rachel Priest ensured New Zealand's chase got off to a solid start with a 58-run opening stand and, from there, the New Zealanders were never under scoreboard pressure as they ticked off the runs with almost four overs to spare.
Bates was thrilled with the victory.
‘‘I am really proud of the way we played today but we are under no illusion that we will win the title,'' the New Zealand captain said.
‘‘We are treating every game as a knockout game.''
‘‘I am sure if we play the way we are, we can win it. If things go our way, we can win it. But we are not looking too far ahead.''
The side has now won all three matches at the championships and plays its final pool game against South Africa on Sunday morning [NZ time].
