The famous rockabilly and country guitarist famously escaped death when he lost his seat on the plane in a coin toss.
Allsup, who also worked as a producer for Willie Nelson, died at a hospital in Springfield, Missouri, on Wednesday, due to complications following a hernia operation.
He rose to fame as part of Buddy Holly’s backup trio after the singer parted from his original band The Crickets.
Holly, one of rock ‘n’ roll’s most prominent figures, died on 3 February 1959 when his private plane crashed near Clear Lake, Iowa.
With him were fellow stars Ritchie Valens and J P ‘The Big Bopper’ Richardson, neither of whom were originally set to travel on the doomed plane.
Richardson had taken the place of country musician Waylon Jennings, while Allsup flipped a coin to see who between him and Valens would get a seat on the plane and who would have to take the bus to the next stop on the tour.
Pilot Roger Peterson, 21, also died in the crash.
The tragedy was later immortalised in Don McLean’s 1971 song American Pie as ‘The Day the Music Died’.
Allsup’s son Austin said his father had always felt lucky to be alive.
“I know my dad has talked about that many times and knew that he was very lucky to be here,” he said. “It could have been the other way around.”
The 32-year-old, who followed in his father’s footsteps and became a musician, said Valens’ sister had been in touch to offer her condolences after hearing of Allsup’s death.
“I told her in my message back, now my dad and Ritchie can finally finish the tour they started 58 years ago,” he said.
Allsup, born in Owasso, Oklahoma, will be buried in his home town on Wednesday.