The winning work, titled Head in the sky, feet on the ground, was made from oil, found textiles and embroidery on canvas, and beat 56 other finalists for the $100,000 prize.
Just 29 years old, Gutman will probably find it hard to keep her feet on the ground after the win. She also becomes the 11th woman to do so.
When Art Gallery of New South Wales director Michael Brand phoned to tell her the news, she was elated.
"Shocked, dumbfounded but very happy. It's honestly completely surreal. I'm so grateful to be working at a time when young female voices are heard," Gutman said.
The artist has been friends with Montaigne for years, having lived in an inner-city share house with the singer, and said they both like to experiment rather than stick to tradition.
The artwork is influenced by Austrian expressionist Egon Schiele, specifically his divisive piece Seated Woman with Legs Drawn Up, which challenged gender norms of the early 20th century.
In Gutman's piece, Montaigne is posed the same way which references her role as a boundary-pushing artist in the 21st century.
"I thought it was a beautiful way to capture Jess, who's queer and dresses in this way that really plays with gender," Gutman told reporters.
Montaigne embodies a marked departure from the Archibald tradition, whose winning portraits often depict older politicians and artists.
Montaigne is young and famous among teenagers, in part because she streams herself performing and gaming on livestreaming website Twitch.
The singer says she never saw the win coming.
"Not because I don't believe in Julia's incredible talent and warm heart but because you just never think this stuff is going to happen to you," Montaigne said.
The work has made Gutman the 100th winner of the award, one of the most prestigious in the Australian art world.
Before her Archibald win, Gutman featured in the Primavera 2022: Young Australian Artists exhibition at the Museum of Contemporary Art Australia and was also a finalist in the 2021 Ramsay Art Prize.
President of the Art Gallery of NSW Trust David Gonski also announced the winner of the institution's other premier prizes on Friday.
The $40,000 Sulman Prize, which goes to the best subject or genre painting, went to Doris Bush Nungarrayi for her acrylic on linen work Mamunya ngalyananyi (Monster coming).
In the painting, Nungarrayi depicts several Mamus, ominous and malevolent spirits that terrify the Anangu people of central Australia.
Zaachariaha Fielding has won the $50,000 Wynne Prize for landscape art with an acrylic on linen work titled Inma, measuring more than three metres across.
The electro-pop musician-turned-artist accepted the award with a smile and a song as he invited members of his team to the stage to perform a soaring vocal interpretation of the winning work.
The painting by the first-time finalist depicts the sounds of Mimili, which is a small community in the Anangu Pitjantjatjara Yankunytjatjara Lands.
For the first time in 2023, there were more works by women (30) than men (27) selected as Archibald finalists.
And including the Wynne and Sulman Prizes, there were more entries than ever from Aboriginal artists, with 101 in total and 38 selected as finalists.
Anne Ryan, the curator of the three prizes, says the winners and finalists reflect the real world.
"Artists from all different backgrounds and different approaches and ideas are out there making work," she told AAP.
"It's really heartening that the Art Gallery of NSW is something they all want to be part of."
The paintings will be exhibited from May 6 to September 3 and then tour until June 2024.
