The portrait of his partner, fellow artist Agatha Gothe-Snape, earned Cairns the $100,000 award.
He was announced as the winner on Friday at the Art Gallery of New South Wales.
The prize is in honour of Victoria journalist JF Archibald, a former trustee of the Art Gallery, who left provisions in his will for an annual portrait prize that began in 1921.
To be eligible, artists must be resident in Australia or New Zealand for a year, enter a portrait that was painted from life in the last year with a subject known to the artist, and preferably with the subject being a man or woman distinguished in art, letters, science or politics.
Cairns, who was born in Camden in 1984, graduated from the National Art School with a Bachelor of Fine Arts in painting and received the 2012 Brett Whiteley Travelling Art Scholarship.
It was the fourth time he had entered his work for the Archibald Prize.
Mr Cairns told the Art Gallery of NSW: "In this painting, Agatha is both an active subject and a recalcitrant muse embracing and resisting simultaneously any idea of what it is to be fixed. Ultimately this is what is most attractive about Agatha.
"She embodies an uncompromising agency whilst having the grace to accept the ready complications inherent within our life as artists."
He explained: "I composed this portrait with love in the full knowledge of its inevitable and palpable quake."
The art gallery's director, Michael Brand, said: "The sensitive portrait carries Cairns' signature playful complexity and this, along with his composition of form and colour, will no doubt draw comparisons with the style of Matisse and other Modernist masters."
Meanwhile the president of the gallery's Board of Trustees, David Gonski, added: "There were many great Archibald contenders this year, but it was the skill and sensitivity of [Cairns'] portrait which left a significant impression on us all."
