Burton, who died in Sun City, California, had been sick for a while, Kelley said. She did not give a cause of death, reported CNN.
Burton, who was once a Golden Gloves heavyweight champion in his native Michigan, played the trainer of Apollo Creed in the first two "Rocky" films, in which Sylvester Stallone's Rocky Balboa took on the Muhammad Ali-like Creed.
In four later "Rocky" films, Evers was in Rocky's corner, helping him defeat such competitors as Clubber Lang (Mr T) in "Rocky III" and Ivan Drago (Dolph Lundgren) in "Rocky IV."
Stallone expressed his feelings on Instagram.
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"Tony Burton who played the character of Duke brilliantly in all six Rocky movies. Rest in peace," he wrote.
Burton had a varied career in Hollywood, guest-starring in dozens of TV series including "The Incredible Hulk," "The Fall Guy" and "Frank's Place", and appearing in a number of movies.
In Stanley Kubrick's 1980 production of "The Shining," he played a garage owner; he also had roles in 1986's "Armed and Dangerous" and 1991's "Hook."
Burton came to acting from an unusual place: prison. He served 3 and a half years in a California institution for robbery.
He participated in a group that used acting exercises and found the emotional outlet powerful.
Burton is survived by his wife and daughter.