McQuagg died at St. Francis Hospital, Sam McQuagg Jr. told The Associated Press.
Preliminary medical reports show McQuagg died from cancer.
McQuagg began racing in the 1950s and entered his first NASCAR race in 1962.
His son remembered his father's racing career as something that seemed normal to McQuagg Jr. and his brother.
"We both grew up around racing," McQuagg Jr. said. "It was how Daddy supported us when we were kids."
In 1966, McQuagg claimed his only NASCAR victory, winning the Firecracker 400 at Daytona International Speedway.
In the 1965 Southern 500, McQuagg was involved in a spectacular wreck that sent Cale Yarborough tumbling over a guardrail. Footage of the crash was later used to illustrate the agony of defeat on "ABC's Wide World of Sports."
McQuagg drove in his last NASCAR race in 1974 and worked as a corporate pilot until retiring in 1997, McQuagg Jr. said.
After retiring, McQuagg traveled the country with his wife, Joy, in a motor home. The couple celebrated their 54th wedding anniversary while he was in the hospital on New Year's Eve.
"He was just a really great down-to-Earth, very loyal guy and I've got to say, we're all going to miss him immensely," his son said.
McQuagg is survived by his wife, two sons, a daughter and four grandchildren.
Funeral services are scheduled for Tuesday.
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