Yonakor grew up in the Dorchester neighborhood of Boston, Massachusetts, the youngest son of immigrants from Russia. At the age of 10, he came down with a leg infection after cutting himself while ice skating. He was too embarrassed to tell his mother about the injury and hoped it would go away, but it worsened to the point where he could no longer walk. Doctors drained fluid from his body by puncturing his toe, and Yonakor spent a year as an invalid; doctors told him he may never walk again. Starting out by crawling, however, Yonakor gradually regained his strength and his health. He went on to play three seasons of football in high school, and spent one year at Marianapolis Preparatory School in Thompson, Connecticut at the prompting of Frank Leahy, then the head football coach at Boston College. Yonakor was set to go to Boston College, but chose the University of Notre Dame instead when Leahy became head football coach there in 1941.
Creighton Miller, a teammate of Yonakor's at Notre Dame, took an assistant coaching position after the war with the Cleveland Browns, a team under formation in the new All-America Football Conference (AAFC). While Yonakor selected by the Philadelphia Eagles in the first round of the 1945 NFL Draft, Miller convinced him to sign with the Browns instead. The Browns won the AAFC championship in each of the four years Yonakor played for the team between 1946 and 1949. He started out as primarily a pass-rushing defensive end in 1946, but was also used as an offensive end when receiver Dante Lavelli was injured in 1947. After watching one of the Browns' early games, Leahy said that the Browns were good, but "I don't understand why they don't throw more passes to Yonakor". He had just six receptions for 95 yards and two touchdowns in 1947, however, and was shifted back to working mostly on defense in 1948. Yonakor completed coursework at Notre Dame between seasons with the Browns and got his degree in 1948. Yonakor got into contractual disputes three times with Paul Brown, the Browns' head coach and general manager, and frequently held out for raises. His highest salary with the Browns was $9,500 in 1949.
Yonakor went back home to Boston after ending his football career and worked in several sales jobs he found unsatisfying. He planned to go to California to find work, but stopped off in Cleveland on the way to make some money for the journey onward. He worked briefly in the structural iron business before getting a job in 1956 at Republic Steel, then one of the country's largest producers of the metal. He was promoted in 1959 to superintendent of Republic's general labor department and oversaw more than 500 workers. He got married and settled down in Cleveland, attending Browns games as he worked at Republic. "I learned teamwork and got used to being around men and learning to get along with them," he said in 1960. "Out here at Republic we operate on the same theory as the Browns – all for one and one for all."
^Sauerbrei, Harold (August 29, 1948). "Lavelli Injured; Out For 6 Weeks". Cleveland Plain Dealer. p. 3C. Brown chooses to experiment with Gillom as his offensive right end rather than John Yonakor because of the former Notre Dame star's value on defense.
^ abc"Yonakor, Ex-Brown, Promoted by Republic". Cleveland Plain Dealer. January 29, 1959. p. 28.
^ abcLustig, Dennis (August 15, 1971). "Young Yonakor Stars as Little League Hurler". Cleveland Plain Dealer. p. 2C.
^"Yonakor Is Sold To Grid Yanks". Cleveland Plain Dealer. August 28, 1950. p. 20.
^"Montreal Signs Yonakor". Cleveland Plain Dealer (Montreal). Associated Press. July 25, 1951. p. 19.
^Sauerbrei, Harold (October 22, 1952). "Browns Wary of Redskins' Williams, Who Raced Kickoffs Back 100 and 95". Cleveland Plain Dealer. p. 31. Among the old-timers is John Yonakor, who played end for the Browns during four years in the All-America Conference. John has been used at both end and tackle by the Redskins.
^ abcdHeaton, Chuck (February 14, 1960). "Ex-Brown Yonakor Returns to Win Job, Wife". Cleveland Plain Dealer. p. 6C.
^Hickey, William (December 3, 1964). "This sporting life...". Cleveland Plain Dealer. p. 70.