The previous record had been set just the day before when a painting by Mark Rothko called Homage to Matisse was sold at a rival auction for $22.4m. A painting by Damien Hirst also broke the record for paintings by the British artist.
After the Wednesday sale of the Smith sculpture, Tobias Meyer, head of contemporary art at Sotheby's, said: "It was the best contemporary-art sale we've ever had."
He said there had been a depth of bidding and global buying as factors which drove up the final price for the sculpture, which had been expected to raise just half of what it fetched.
After a round of fierce bidding, the sculpture, last of a group of 28 large-scale works made by Smith, and one of only seven not in museums, was eventually bought by the Manhattan dealer Larry Gagosian. It was sold by a foundation owned by Sid Bass, the Texas oil heir and financier.
The final price for the 1965 Smith sculpture was nearly five times the artist's previous record. Smith died the same year in which he completed the massive work, which evokes a gate or an arch.
The auction completed two weeks of successful sales at Sotheby's and rival Christie's, which sold the Rothko painting.
Most of the auctions topped their high-end pre-sale estimates, which experts said was something that has not occurred in recent memory. Works by other artists, including Andy Warhol and Cy Twombly also sold well, with the record for Twombly broken twice.
Warhol's Jackie Frieze, a series of 13 silkscreens of President John F Kennedy's widow Jacqueline in mourning, rendered in white or varying shades of blue, sold for $9.2m. Another iconic image, 1964's Flowers sold for $6.7m.
Other artists whose work broke records included Hiroshi Sugimoto, Francis Alys, Vija Celmins and Louise Bourgeois, whose "Spider" sculpture sold for just more than $3m, doubling her record.
Damien Hirst's painting, The Most Beautiful Thing In the World fetched $1.3m at the auction, a record price for his paintings.
Only six of the 54 lots at Sotheby's failed to sell.