Australia made New Zealand pay for a below-par total by reaching a target of 220 for the loss of five wickets with eight balls to spare at Bristol.
Ellyse Perry, who made her name as a fast bowler, scored 71 as she reached the landmark of 2 000 one-day international runs.
"Today has been our biggest test against a fantastic team in New Zealand, they always give us a tough game," said Perry.
India were held to 169 for nine by Pakistan at Derby only to bowl out their arch-rivals for just 74 for a 95-run win, with left-arm spinner Ekta Bisht taking five for 18.
"She’s delivered time and again for India and I'm very proud of her," said India captain Mithali Raj of Bisht.
Earlier, West Indies, the reigning World Twenty20 champions, slumped to a 10-wicket defeat by South Africa as their campaign suffered a new low in Leicester.
Chedean Nation, with 26, was the only West Indies batsman to make double figures as South Africa captain Dane van Niekerk became the first bowler, in either men's or women's international cricket, to take four wickets without conceding a run in her final figures.
'SURREAL'
But the real damage to the West Indies' hopes was done by Marizanne Kapp and Shabnim Ismail, who reduced the Caribbean side to 16 for five.
Kapp took 4-14 and van Niekerk an astonishing 4-0 in 3.2 overs.
"It was quite surreal, if I could script it I would not have written it like that," said Van Niekerk.
Chedean Nation, with 26, was the only West Indies batsman to make double figures as South Africa captain Dane van Niekerk became the first bowler, in either men's or women's international cricket, to take four wickets without conceding a run in her final figures.
'SURREAL'
But the real damage to the West Indies' hopes was done by Marizanne Kapp and Shabnim Ismail, who reduced the Caribbean side to 16 for five.
Kapp took 4-14 and van Niekerk an astonishing 4-0 in 3.2 overs.
"It was quite surreal, if I could script it I would not have written it like that," said Van Niekerk.
