Healy’s 53 off 38 balls was crucial to Australia’s 7-153, leaving a record run chase for the White Ferns.
The Aussie attack then ripped through the Kiwis, taking three wickets in the first three overs as New Zealand slumped to 3-13 - their chase seemingly over before it began.
But a fightback led by Adelaide Strikers gun Suzie Bates almost thwarted Australia’s quest for a third straight win.
Bates was dropped by Healy on 27 in the 10th over and added 66 for the fourth wicket with Katey Martin (24 from 20) to leave the Aussies with more than a few nerves in the middle overs.
But their innings changed once Healy produced a sparp moment of keeping, whipping the bails off to have Martin stumped off Georgia Wareham - leading to a regular run of wickets before New Zealand were rolled for 120 with 15 balls to spare.
The death knell was the exit of Bates, who fell lbw to Ashleigh Gardner's off-spin for a well-made 48 off 44.
Schutt took 3-12 off three overs, while Sophie Molineux and Delissa Kimmince both added a pair of wickets.
Australia plays India on Sunday morning (AEDT), but are now booked for an Antigua semi-final regardless of the result of he final pool game.
If India beats Ireland later this week, which is very likely, weather permitting, they will have also qualified for the final four ahead of the clash with the Aussies.
HEALY STILL IN THE RUNS
In-form opener Alyssa Healy was slow to begin, but after being dropped by New Zealand leggie Amelia Kerr at point in the third over on 11 runs, she made the most of the chance.
Healy posted her second half century of the World T20 , her 50 coming off 33 balls, and now has the most runs of any other player in the tournament (157 at an average of 78.5).
While she appeared to have her eye well and truly in, she was bowled on 53 after completely missing a ball on leg stump.
Healy had been starved of the strike in the lead up to the wicket, facing just eight balls in four overs.
HAYNES HONES IN
Rachael Haynes asks herself before every innings: ‘ If this was my last ever game, how would I want to play?’
Like she did tonight would be just fine.
The 31-year-old vice-captain came in with her side 4-108 in the 14th over and while her teammates crumbled around her, Haynes kept her head and ploughed on.
A beautiful pull shot for four, where she rolled her wrists and hit the ball backward of square, was a highlight of her innings.
She carried her bat for 29 off 18 balls.
STRIKE RATE RULE
Australia wants its best strikers at the top of the order and the benchmark number is 120.
Any less, and you’re just wasting everyone’s time.
While Healy was strong with a strike rate of 139, fellow opener Beth Mooney was at 108 and Meg Lanning, who came in at No. 3, was at 83. Ashleigh Gardner made 10 off 13 with a strike rate of 76.
Australia still posted 7-153 and set the White Ferns a record run chase, but to win this tournament they’ll need to step it up.
BOWLERS START WELL... AND THEN?
Megan Schutt was mad at herself after being taken to by the Irish earlier this week and started the game with a five-run wide. But with her fifth ball she trapped Anna Peterson for a duck, and all was forgotten.
The tear away was slapped around by Ireland, finishing the game with the figures of 1-30 but responded against the Kiwis with the impressive numbers of 3-12.
Ellyse Perry clean bowled Sophie Devine in the second over and Victorian Sophie Molineux chimed in with the wicket of her Renegades captain Amy Satterthwaite in the third as the Kiwis slumped to 3-13.
But the Aussie attack let Susie Bates take hold, with the White Ferns opener making 48 off 44 and almost stealing the show.
Originally published as Australia nail World T20 semi-final spot with 33 run victory over New Zealand
Updates
In the end, a pretty dominant victory to Australia despite looking a little hairy while Suzie Bates and Katey Martin were rolling along in their 66-run partnership.
Once Georgia Wareham removed the dangerous Martin, brilliantly stumped by Alyssa Healy, the writing was on the wall and New Zealand lost regular wickets.
Megan Schutt returned to clean up the tail and finished with three wickets.
But it was built around the outstanding batting of Alyssa Healy who nabbed her third player-of-the-match award with another half century.
In the end, a pretty dominant victory to Australia despite looking a little hairy while Suzie Bates and Katey Martin were rolling along in their 66-run partnership.
Once Georgia Wareham removed the dangerous Martin, brilliantly stumped by Alyssa Healy, the writing was on the wall and New Zealand lost regular wickets.
Megan Schutt returned to clean up the tail and finished with three wickets.
But it was built around the outstanding batting of Alyssa Healy who nabbed her third player-of-the-match award with another half century.
Hannah Rowe is swinging wildly – and should've been caught at mid-off by Kimmince who spills a simple looped chance.
But she gets done by the straight one…. and Schutt knocks over the stumps as Rowe walks down the pitch.
Two wickets from that over leaves New Zealand requiring 36 runs from the final three overs.
It's a big ask.
Hannah Rowe is swinging wildly – and should've been caught at mid-off by Kimmince who spills a simple looped chance.
But she gets done by the straight one…. and Schutt knocks over the stumps as Rowe walks down the pitch.
Two wickets from that over leaves New Zealand requiring 36 runs from the final three overs.
It's a big ask.
Leigh Kasperek's dangerous little cameo comes to an end with the first ball of Schutt's new spell.
A slower bouncer is clipped to Rachael Haynes at point.
Kasperek hit two boundaries and finishes with 12 from 7 – but leaves with a huge job to be done.
The end is nigh…
Leigh Kasperek's dangerous little cameo comes to an end with the first ball of Schutt's new spell.
A slower bouncer is clipped to Rachael Haynes at point.
Kasperek hit two boundaries and finishes with 12 from 7 – but leaves with a huge job to be done.
The end is nigh…
Four overs to go now, with just four coming from that Kimmince offering – including a wild overthrow on the last ball!
And Australia brings back their best bowler, Megan Schutt.
She may have just given up 11 runs – including a boundary to Kasperek who pulls off one of the shots of the night with a lofted cover drive – but by getting the wicket of Suzie Bates, Gardner should've sealed the game for Australia there.
43 from 30 balls required looks gettable – but wickets are drying up.
That should be enough for Australia, with the dangerous Suzie Bates trapped LBW just short of her half century.
Gardner sent down a quicker delivery and beat Bates for pace – with the veteran walking down the wicket before getting smacked on the pad.
A fine knock comes to an end on 48 from 42. New Zealand now 7-99, still 53 runs required.
That should be enough for Australia, with the dangerous Suzie Bates trapped LBW just short of her half century.
Gardner sent down a quicker delivery and beat Bates for pace – with the veteran walking down the wicket before getting smacked on the pad.
A fine knock comes to an end on 48 from 42. New Zealand now 7-99, still 53 runs required.
