A Rodin sculpture that a Potomac family owned for decades without knowing that it was genuine sold for $306,800 at an auction Saturday in Falls Church.

The bronze-and-marble sculpture of a woman crossing her legs once shared space with Elizabeth Tillson’s family’s gerbil. It was only recently that Tillson and her siblings learned that the work is an original by French sculptor Auguste Rodin, whose work is in museums in Paris and Philadelphia.

The green cast, “Le Désespoir [Despair],” was item No. 160 at Saturday’s auction at Quinn’s Auction Galleries and was among several fine and decorative art pieces that were sold. One of them, an oil painting by American artist William Foote sold for $17,700, and an eye-shaped clock designed by American George Nelson for the Howard Miller Clock Co., went for $1,888.

Selling the Rodin sculpture took less than three minutes. There were 10 bidders on the phone and three on the floor. Bidding opened at $37,500 and quickly escalated — the next bid was $60,000. From there, they rose in increments of $10,000 to $30,000.

“You could tell the excitement was growing,” said Tillson, 55, who attended the auction with her children and sister. “We were almost in tears. . . . The bids kept going up, and people on the phone kept conversing, and all of a sudden, it was done.”

Bidder No. 18, who was calling in from Germany, won it.

For a long time, Tillson and her family wondered if the sculpture that she remembers from her childhood home in Potomac was real. Last year, a New York auction house offered to sell the 14-inch-tall statue, but because the auctioneers could not authenticate it, the house estimated its sale price at only $1,500 to $2,500.

The family sought a second opinion from Quinn’s Auction Galleries, where Matthew Quinn worked for months validating that it was an original work by Rodin, known for his statue “The Thinker.” It was a difficult task, as Tillson and her siblings had never asked their parents how the sculpture came to be in their home. All they knew was that their grandfather had somehow acquired it before he died in 1960.

Quinn found the raised signature of A. Rodin at the bottom of the sculpture. He then brought the piece to Jérôme Le Blay, who heads the Comité Auguste Rodin and has seen thousands of Rodin’s works, and he validated the sculpture as an original.

Quinn had estimated that the piece could sell for up to $200,000. Two similar versions sold at auction for $192,000 in 2006 and $194,600 in 2011, he said.

“The fact that we were able to beat those by over $100,000 is really impressive,” Quinn said.

Tillson and her two siblings will probably split the proceeds, she said, adding that she plans to use some for a family trip and perhaps buy a convertible. A special family lunch Saturday was the start of the celebration, she said. But before that, Tillson paid a final visit to the sculpture she once thought of as “creepy.”

“I have come to quite love the piece,” she said.

She carefully rubbed the back of the sculpture — “just to wish it luck, and wish us luck.”