The winning work is titled Flagship Mother Multiverse (Justene), and depicts the artist floating among the stars above the materials of making art, her daughter looking on.
Fragar has been a finalist in the Archibald four times, and burst into tears when Art Gallery of NSW director Maud Page called Friday morning to tell her she had won.
"It feels unbelievable, can you imagine? I'm from a small country town originally, I moved to Sydney to go to art school, so to win the Archibald is amazing," Fragar said after the announcement in Sydney.
She described the win as an incredible honour and her longtime friend and colleague Williams as an extraordinary artist.
"I wanted to honour the incredible multiverse of artworks that seems always to be exploding from her, spinning not quite out of control," the Brisbane artist said.
"The work is a reflection on the experience of making art to deadlines and the labour and love of being a mother."
The title of the winning work comes from Williams' recent endurance performance in New Zealand, titled Making do rhymes with poo, about juggling a day job with art making and motherhood.
It's the third year in a row a female artist has won the Archibald, making Fragar the 13th woman to win since the prize started in 1921.
"Here are two of Australia's great artists in conversation about what matters most to them," said Page, who was announced in March as the gallery's new director.
Fragar conducted a photo session with Williams and spent three months in the studio working on the painting, which she hoped would communicate her subject's singularity and otherworldliness.
The winner was selected from 903 entries and 57 finalists, with works painted in the past year from at least one live sitting.
The award, widely regarded as Australia's most prestigious art prize, is judged by the trustees of the Art Gallery of NSW, who made a unanimous decision on Friday.
Jude Rae has won the $50,000 Wynne Prize for landscape painting or sculpture, for the oil on linen work Pre-dawn sky over Port Botany container terminal.
The $40,000 Sulman Prize for genre painting went to Katoomba-based artist Gene A'Hern for Sky painting, beating a record field of 732 entries.
For the first time in 2025, women artists made up the majority of finalists in each of the Archibald, Wynne and Sulman Prize competitions.
Earlier in May, the $3000 Packing Room Prize selected by the gallery's art handling staff went to Abdul Abdullah for a portrait of his friend Jason Phu.
The finalists for all three prizes will be on show at the Art Gallery of New South Wales from Saturday until August 17, before touring Victoria and NSW.
