LONDON—How many paintings does an American museum have to sell to raise funds for a single canvas by Russian modern painter Kazimir Malevich?

Recently, the Art Institute of Chicago sold a quartet of artworks for a combined £10 million ($16.1 million) at Christie’s to help pay for its recent purchase of a painting by Malevich, a pioneer in abstract art.

The museum gave up Georges Braque’s “Still Life with Guitar (Red Curtain)” for £3.9 million and Henri Matisse’s creamy “Woman in an Armchair” for £791,650. It also sold a pair of early Pablo Picasso works, including “On the Upper deck Crossing the Seine,” for £4.8 million.

These four works, which Christie’s priced to sell for a combined £7.2 million or more, were auctioned to help the Chicago museum pay an undisclosed sum for Malevich’s “Painterly Realism of a Football Player—Color Masses in the 4th Dimension,” a jumble of colorful geometric shapes against a white background that the artist created in 1915.

“The Art Institute is very pleased with the results of tonight’s auction,” said institute spokeswoman Erin Hogan. “The four works at Christie’s had been considered for deaccession for some time—because curators felt that we had more important examples by these artists from the respective periods—and the timing was right for us considering the recent availability of a work by Kazimir Malevich.”

Malevich (1878-1935) is known for paving the way for modernism through such early examples of abstract art. He left “Painterly Realism” with friends in Europe a few years before the onset of World War II but died in Stalinist Russia before he could come back to fetch it. The work wound up hanging in the Stedelijk Museum in Amsterdam. It was restituted, along with several others, to the artist’s heirs three years ago.

Gagosian Gallery brokered the sale of “Painterly Realism” between the heirs and the Chicago museum last month.

Sotheby’s sold another of the restituted Malevich paintings from 1916, “Suprematist Composition,” to dealer David Nahmad for $60 million three years ago.

Museums tend to be castigated whenever they hawk wares from their own storehouses, but dealers called the Chicago swap a clever trade: The museum still has plenty of Impressionist and Cubist works in its collection, but this deal makes it the only U.S. museum besides New York’s Museum of Modern Art to boast a Malevich painting.

The deal also helped anchor Christie’s £61.8 million evening sale of Impressionist and modern art. That total fell midway between its presale expectations of £54.7 million to £81 million. Rival Sotheby’s brought in £68.8 million from a smaller sale of art from the same era the night before.

Besides the Chicago works, the biggest drama of the night came when Christie’s failed to sell its priciest piece, Paul Gauguin’s “Still Life with ‘Hope.’ ” The work was expected to sell for between £7 million and £10 million but stalled at £5.8 million and went unsold.

Collectors chased harder after Edgar Degas’ 1896 pastel, “Dancers in Yellow Skirts (Two Dancers in Yellow),” a charming glimpse of two back-stage ballerinas. It was priced to sell for up to £5 million but wound up selling to a telephone bidder for £5.4 million.

André Derain’s “Boats in Collioure,” a Fauve coastal scene dominated by a red, earthen foreground, sold for £5.8 million. It was expected to sell for between £4 million and £6 million.

A pair of telephone bidders — one from Russia — got into a lengthy bidding war over Pierre Bonnard’s “Terrace at Vernon,” a large sun-dappled landscape that was only expected to sell for up to £4 million. The Russian collector wound up winning it for £7.2 million, a new auction record for the artist.