A stylish 60 from Beth Mooney and controlled bowling Monday kept intact Australia's record of making at least the semi-finals of every Twenty20 World Cup in a nail-biting four-run win over New Zealand.

The defending champions and four-time winners join India, England and South Africa in the last four, with the games played in Sydney on Thursday.

Australia have been dominant since the World Cup was introduced 11 years ago, but were upset by India in the opening game of the tournament.

Rattled, they bounced back emphatically against Sri Lanka and Bangladesh before narrowly accounting for their trans-Tasman rivals, who leave the World Cup empty-handed.

The White Ferns won the toss and bowled at Junction Oval in Melbourne, snaring an early breakthrough. But Australia has incredible depth in its batting and Mooney led them to a competitive 155 for five.

Skipper Sophie Devine (31) and Katey Martin (37) led the chase, but Australia's bowlers were up to the task, with spinner Georgia Wareham taking three crucial wickets.

"It was a crunch game and I thought we handled it really well," said skipper Meg Lanning.

"I think we showed that we are able to be calm under the pump, we have done the basics right which gives us confidence going into the semi-finals."

One worry for Australia is the fitness of the world's top T20 all rounder Ellyse Perry, who limped off while fielding, seemingly with a hamstring problem.

New Zealand removed the dangerous Alyssa Healy cheaply with Lanning joining Mooney, but after an attacking 21 she was caught off Anna Peterson's bowling.

Ashleigh Gardner (20) shared in a quickfire 52-run stand with Mooney, who brought up her fifth half-century in nine innings off 42 balls.

Playing in her 50th T20, Moody finally departed for 60, but it needed a spectacular catch on the boundary from Suzie Bates to remove her.

Perry (21) and Rachael Haynes (19) added crucial late runs to power the score past 150. 

Rachel Priest looked dangerous as New Zealand set about the chase, hitting quick three fours, but she was undone by Jess Jonassen.

Australia piled pressure on when Wareham snared the world's number one T20 batswoman Bates for 14, leaving them in trouble on 55 for two at the halfway mark.

Devine knew she had to take risks and after reaching 31 charged down the wicket to Wareham and was stumped.

Maddy Green took on the attack in a lightning 28 but Wareham again pounced, with her wickets proving vital as New Zealand fell short.

A legend

Earlier, Sri Lanka ended their tournament on a high with a crushing victory over Bangladesh in a fitting farewell to retiring veteran Shashikala Siriwardena, who bagged a tournament-best 4-16.

The clinical nine-wicket win was their first of the event to leave them fourth in Group A, with Bangladesh beaten in all four games to prop up the table.

While neither team could reach the knockouts, there was plenty at stake with the winner avoiding having to qualify for the 2022 tournament in South Africa by virtue of finishing as one of the top eight sides.

"Really happy with the performance." said Sri Lanka captain Chamari Atapattu, who paid tribute to Siriwardena.

"She's a legend in Sri Lanka and she's the big sister of the Sri Lankan team. I will miss her a lot, but she retired like a champion." 

Bangladesh won the toss but again failed to fire.

None of their players managed a half-century during the tournament, with Nigar Sultana Joty once more the standout, smacking 39 in their 91 for eight.

Siriwardena was the top bowler in her last match after a 17-year international career.

Sri Lanka made a good start with Atapattu crunching 30 before being stumped.

Fellow opener Hasini Perera (39 not out) and Anushka Sanjeewani (16 not out) kept the momentum going to cruise home with 27 balls left.