Central Stories Museum and Art Gallery general manager Maurice Watson announced the campaign in the Otago Daily Times last week and the required funds were raised within two days of the story being published, Mr Watson said.
He praised the museum and wider Alexandra community for its support and donations.
Stevens, who died in 2009, was one of Central Otago's most important artists, Mr Watson said.
The museum already owned about 40 of her artworks, but the painting being bought - Differing Realities - was especially significant because of a letter written by Stevens on the back of the painting, he said.
In the letter Stevens wrote about ''how she sees the world and how she is trying to paint'', and her words took viewers ''inside the mind of a working artist'', Mr Watson said.
The $3000 will pay for the purchase, transport, insurance and conservation of the painting.
Central Stories is working with Stevens' family and seeking other artworks for an exhibition of her work planned later this year.
