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?"
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