Crowe owns a sheep and cattle ranch in Australia
Four antipodean actors, including Russell Crowe and Nicole Kidman, took away acting awards, while Moulin Rouge - made in Sydney by Australian director Baz Luhrmann - won a total of three.
But New Zealand's most famous production, The Lord of the Rings, lost out in the best dramatic film category.
Crowe, who was born in New Zealand but spent most of his life in Australia, was named best dramatic actor for his role as a schizophrenic mathematician in A Beautiful Mind.
"G'day folks. How ya doin'?" he said on taking the platform to accept the award.
Cinema is "held very dear" by audiences in Australia, he said.
"It's an indication that we may be a long way away but we all have the modern technology. We try to keep up with it."
The antipodean contingent was so closely-knit that they wanted to sit together at the ceremony - but the Hollywood Foreign Press Association, which organises the event, refused the request.
"They wouldn't let us. We would have been too rowdy," Kidman said.
Sydney studios
"Aussie! Aussie! Aussie!" came the cry from Moulin Rouge director Baz Luhrmann.
Luhrmann lost out in the best director category, but his film - made at Sydney's Fox Studios - was named best musical or comedy.
Another Australian actress to fly the flag was Rachel Griffiths, a surprise winner as best supporting actress in a mini-series or TV movie.
Griffiths - honoured for her role in dark TV comedy Six Feet Under - beat competition from the likes of Friends's Jennifer Aniston, The West Wing's Allison Janney and Will and Grace's Megan Mullally.
The first words of her acceptance speech were: "Oh my God. I'm not tanked but I'm legless."
Griffiths has been seen in films including Blow, Muriel's Wedding, Very Annie Mary and Hilary and Jackie.
Judy Davis, another victorious Australian, had been nominated twice before but this year was named best actress in a mini-series or TV movie for playing the title role in Life With Judy Garland: Me and My Shadows.
She thanked "my beautiful homeland, Australia, and the creative community there".
"When I first came to America there were people who thought I was from Austria."
Kim Dalton, chief executive of the Australian Film Commission, said the victories are "something that all Australians should be proud of".
The awards were good news for the profile of Australian film and television and the profile of the nation as a whole, he said.
And the country seems to have a number of rising stars who could make an impact in future years, such as Hugh Jackman - who was nominated as best actor in a musical or comedy this year - plus actors Heath Ledger, Eric Bana and Guy Pearce and director Gregor Jordan.
But those within the country's film industry should not get too excited, Strictly Ballroom producer Tristram Miall says, as this year's success may be no more than a passing phase.
"It may mean that people will take a call from an Australian producer or director, and so on, but at the end of the day it comes down to the particular project and the passion of the people wanting to make it," he says.
"These things sort of go up and down, they are cyclical and it may well be that next year is not nearly as good for Australian performers."