After college, Kavanaugh signed a minor league baseball contract with the St. Louis Cardinals organization for $300 a month. He later signed with the NFL's Chicago Bears after striking a deal with Bears owner George Halas for $300 a game. He played for the Bears during a period in which they were nicknamed the Monsters of the Midway. In the 1940 NFL Championship Game, the Bears defeated the Washington Redskins 73–0, the most lopsided victory in NFL history. Kavanaugh caught the game's only touchdown pass, a 30-yard reception from quarterback Sid Luckman shortly before halftime. The next season, the Bears won the 1941 NFL Championship Game, as they defeated the New York Giants 39–7 and repeated as NFL champions. The final score in the game was a fumble recovery by Kavanaugh on defense, returning the ball 42 yards for a touchdown. In his first two seasons with the Bears, Kavanaugh compiled 23 receptions for 590 yards and nine touchdowns.