The final was tense throughout and came down to the dying seconds and just one goal, as the Kiwis prevailed 52-51.
It was the Silver Ferns' fifth world title but their first since 2003 as they finally ended the Diamonds' dominance.
England clinched bronze with a 58-42 victory over South Africa in their play-off match earlier on Sunday.
The Roses' win was routine compared with the drama which followed between the Trans-Tasman rivals who were competing against each other for the sixth consecutive World Cup final.
In a final that was evenly poised at half-time, New Zealand came out firing in the third quarter as they powered into a seven-goal lead with the 8,000-strong crowd behind them.
Australia reached the final unbeaten, defeating the Silver Ferns in their last group game by a single goal, and they brought the score back to that margin in the fourth quarter as Liverpool prepared for a spectacular finish.
But then they wilted under the pressure. With three minutes remaining, a mistake between the usually reliable shooter Caitlin Bassett and wing attack Kelsey Browne left the Diamonds flustered and New Zealand secured the turnover.
The Silver Ferns held their nerve and ran the clock down to snatch the trophy from their long-time rivals.
It gave a number of players the perfect send off, with Kiwi veteran defender Casey Kopua and international centurions Laura Langman and Maria Folau likely to bow out as world champions.
Kiwi coach Noeline Taurua, who took charge 11 months ago, suggested that her more experienced players were central to the victory. She said: "Our fossils stood up and led from the front.
"I was actually quite speechless. Every day was going to be a challenge for us. To do the final is massive for the Ferns, for the sport and the community at home."
Australia coach Lisa Alexander chose to start captain Bassett after resting her for the semi-final against South Africa and she said after their defeat: "There are hundreds of things you could change to make a difference but I'm proud of our efforts. We just didn't bring our A game.
"We'll look at everything but you don't have a knee-jerk reaction on a one-goal loss. It shows how close world netball is."
The Diamonds have now lost back-to-back major finals following their defeat by England in the Commonwealth Games in 2018, which also ended 52-51.