He TKO'd El Paso Golden Gloves Heavyweight Champion and karate black belt, David Ochoa, in the first-ever professional kickboxing event in El Paso, Texas, in 1975. The promoters were Robert Nava and boxing trainer Tom McKay under the guidance of boxing guru and matchmaker, Paul Clinite. Clinite signed Randall to a professional-boxing contract a few weeks later. He also signed Ochoa, who had fought amateur under the guidance of McKay as his trainer. Clinite provided films of heavyweight boxers to study to get the huge Cobb a good style. After a few days, it was decided that Randall should work at learning the "Joe Louis shuffle". Randall, Paul, and Tom spent a few months at El Paso's San Juan Boxing Gym just doing the simple basics. A few months later, Clinite made arrangements for Randall to be sent to Joe Frazier's gym in Philadelphia.
After nine straight wins as a Kickboxer, Cobb lost his first two amateur bouts. In his professional-boxing debut on January 19, 1977, in El Paso, he knocked out Pedro Vega. He went on to win 13 straight fights by 1979, all by knockout. Cobb was a fighter who had hitting power, as shown by his eighth-round knockout victory over Earnie Shavers in 1980. He lost his two following bouts to Ken Norton and Michael Dokes, respectively, but soon bounced back to earn a shot at Larry Holmes' WBC World Heavyweight Championship. On November 26, 1982, at Houston's Astrodome, Cobb was defeated in a unanimous decision by Holmes, who won all 15 rounds on two of three scorecards. The bloody one-sidedness of the fight, which came 13 days after the bout between Ray Mancini and Duk Koo Kim that led to Kim's death four days later due to brain trauma, so horrified Sportscaster Howard Cosell that he vowed never to cover another professional match, which Cobb jokingly referred to as his "gift to the sport of boxing." When prodded further regarding Cosell's remarks, Cobb observed, "Hey, if it gets him to stop broadcasting NFL games, I'll go play football for a week, too!" When asked if he would consider a rematch, Cobb replied that he did not think that Holmes would agree, as Holmes' "hands could not take it." In an interview after the Holmes fight, he was asked how he could fight someone whose arms were a foot longer than his were, to which he replied, "Oh, it seemed that way to you too?"
Cobb lives in Philadelphia, and maintained a friendship with Philadelphia Daily News columnist Pete Dexter, who frequently commented on boxing. In a notorious 1981 Grays Ferry incident, Cobb came to the defense of Dexter, who during the course of a bar brawl, was severely beaten. Cobb rescued him and endured a broken arm, costing him a scheduled fight with Muhammad Ali. Ali then fought Trevor Berbick and lost.
He made a brief return to kickboxing on May 5, 1984, to challenge John Jackson for the Professional Karate Association United States Heavyweight title in Birmingham, Alabama, losing on points. Between late 1984 and 1985, he lost four straight fights, the last of which was a knockout at the hands of Dee Collier, the only time he was ever KO'd. After a two-year hiatus, he made a return to the ring and went on a 20-fight undefeated streak against lightly regarded opponents (including a win over past-his-prime former champ Leon Spinks in 1988) before retiring again rather suddenly in 1993. A 1993 Sports Illustrated article alleged that Cobb had participated in a fixed fight with Sonny Barch and had used cocaine with Barch and promoter Rick "Elvis" Parker before and after the fight. Cobb said the magazine libeled him, and he sued for US$150 million. In 1999, a jury awarded Cobb $8.5 million in compensatory damages and $2.2 million in punitive damages. However, the verdict was overturned in 2002 by a federal appeals court, which said that the article was not published with "actual malice". The magazine did not interview the Referee and other ringside officials who were at the match, which tends to show that the magazine "might not have acted as a prudent reporter would have acted", the ruling stated. "But the actual malice standard requires more than just proof of negligence".
In January 2008, at age 54, Cobb graduated magna cum laude from Temple University with a bachelor's degree in sport and recreation management. He remarked that it was odd to hear the cheers of a packed arena without being in a boxing ring. "It was nice to have that opportunity to wear a robe, to step up there and not have to worry about bleeding", Cobb said. Cobb's eldest son Bo was killed in an accident in early 1999. His younger son Joshua pursued a short career as a boxer.
Randall Cobb was born in Bridge City, Texas, the son of Norma Grace (née Alexander) and Williard Glynn Cobb, a factory foreman. He was raised in Abilene, Texas, and attended Abilene High School, where he played on the football team. Cobb later studied at Abilene Christian University, but dropped out at the age of 19, and began karate training. He lived in the dojo, cleaning the mats to earn his keep. After earning his black belt, he craved full-contact competition, thus took up kickboxing, fighting in an era when only full contact rules were used in the United States. He won his first nine matches, going 9–0 with all knockouts.