Two people on the telephone bid against each other for nine minutes before the hammer came down, the auction house said. The buyer's identity wasn't disclosed.
The painting had a pre-sale estimate of $15 million to $20 million. In 2006, the auction house sold Rockwell's "Breaking Home Ties" for more than $15 million, then a record.
The previous record for any work at an auction of American art was set in 1999, when George Bellows' painting "Polo Crowd" sold at Sotheby's for $27.7 million, the auction house said.
Another Rockwell painting, "The Gossips," sold Wednesday for just under $8.5 million, while a third, "Walking to Church," fetched a little more than $3.2 million.
For nearly two decades, all three had been on loan at the Norman Rockwell Museum in his hometown, Stockbridge, Mass. The museum has the world's largest collection of original Rockwell art.
Rockwell was paid $3,500 for "Saying Grace," which appeared on the cover of the magazine's Thanksgiving issue in 1951 and was voted Post readers' favorite cover in a 1955 poll.
The idea for the illustration came from a reader who saw a Mennonite family praying in a restaurant. Rockwell's son Jarvis Rockwell was among the models he used for it.
The illustrator, who created his first cover for the Post in 1916, is celebrated for his reflections of small-town America and portraits of famous figures. He spent 47 years at the magazine and produced 321 covers. He died in 1978.
"The Gossips," which was a cover illustration for the March 6, 1948, issue, depicts a montage of the artist's neighbors, his wife and himself, finger-wagging and yammering on the phone.
"Walking to Church" appeared on the cover of the April 4, 1953, issue and shows a family dressed in its Sunday best walking along a city street.
The three paintings, along with four other Rockwell works, were auctioned by the family of Kenneth Stuart, Rockwell's longtime art director at the magazine. The sale comes years after a legal fight among Stuart's three sons. Rockwell and Stuart worked together at the magazine for 18 years.
Rockwell Museum director Laurie Norton Moffatt, who attended the "Saying Grace" auction, called it "a thrilling moment for Norman Rockwell."
"It's a painting of such significance that, wherever it is, there will hopefully be a desire to share it, have it seen in public," she said.
She said perhaps it will go on loan or be placed in another museum exhibition.
"We're just so happy we were able to share it for two decades," she said.
The auction record for a work by any American artist goes to Andy Warhol's painting "Silver Car Crash (Double Disaster)," which sold at Sotheby's last month for $105 million.