user: The musician famously lost a coin toss for a seat on the plane. His place was taken by teen star Ritchie Valens, who also perished when the plane crashed.
Allsup went on to become a Grammy-winning musician, who played with Merle Haggard, Roy Orbison and Willie Nelson.
He said he thought about the crash, and thanked God, every day of his life.
The musician died on Wednesday at a hospital in Springfield, Missouri, due to complications from a hernia operation, said his son Austin.
"Tommy Allsup was one of western swing and rockabilly music's finest," said Neil Portnow, president of the Recording Academy. "The Oklahoma native and was admired by his peers and fans alike [and] heralded by Paul McCartney as one of the finest guitar players in the world.
"Our deepest condolences go out to Tommy's family, friends, and creative collaborators."
Born Tommy Douglas Allsup in 1931, the musician was the 12th of 13 children, and an enrolled member of the Cherokee Nation.
He grew up in Owasso, Oklahoma - a tiny town with a population in the hundreds before it became a centre for the airline industry in the 50s.
When he was 16, he would hitchhike to Cain's Ballroom in Tulsa to watch early rock and roll shows.
"I was six foot tall, and back then they didn't even have IDs," he local newspaper Tulsa World last year. "If you were big enough to stand up to the bar, you could get you a beer."
Eventually, he plucked up the courage to perform at the venue himself and, by the mid-50s, he was a jobbing musician. He met Buddy Holly in a recording studio in 1958, and the star invited him to join his band on the fateful Winter Dance Party tour a year later.
Crossing Midwest America in freezing conditions, many of the musicians succumbed to the flu and even frostbite. To avoid one particularly wintry bus journey, Holly decided to charter a plane between Clear Lake, Iowa and their next venue in Minnesota.
Allsup was originally supposed to catch the flight, but Valens - who had previously suffered a fear of flying - pestered him to swap places.
"He asked me four or five times could he fly in my place," Allsup recalled in 2007.  "For some reason, I pulled a half dollar out of my pocket and flipped it. He said 'heads' and it came up heads.
"So I went out to the station wagon and told Buddy. I said, 'I'm not going. Me and Ritchie flipped a coin. He's going in my place'. Buddy, said 'cool'."
The plane crashed shortly after take-off in the Iowa countryside.
Allsup was initially listed as one of the victims, as he had given his wallet and ID to Holly, asking him to pick up some mail from the post office when he landed in Minnesota.
"When they found the bodies the next morning, they found five wallets with five different IDs," Allsup said. "So they had my name on Associated Press as one of the people on the plane."
The crash was later immortalised in Don McLean's song American Pie, and became known as "the day the music died".
Austin Allsup said his father took losing the coin toss as "a blessing" and that he was humbled to be connected to "such a monumental moment in music history".
He added that Valens' sister had contacted him after his father's death to offer her condolences.
"I told her in my message back, now my dad and Ritchie can finally finish the tour they started 58 years ago," he told ABC news.
Allsup's friend Randy Steele said the star "got an additional 57 years and 11 months" out of the coin flip and "used it for good".
"I was literally in awe of him, not just because of his talent, but because of the kind of man he is."
Funeral services are expected to be held next week and Allsup will be buried in Oklahoma, near his home town of Owasso.
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assistant: Rockabilly guitarist Tommy Allsup, who narrowly avoided boarding the plane that killed Buddy Holly and the Big Bopper, has died aged 85.