A pinpoint passer, Dawson's mobility helped him flourish in Stram's "moving pocket" offense. He would win four AFL passing titles and was selected as a league All-Star six times, ending the 10-year run of the league as its highest-rated career passer. From 1962 to 1969, Dawson threw more touchdown passes (182) than any other professional football quarterback. In 1966, Dawson led the Chiefs to an 11-2-1 record and a 31-7 win over the Buffalo Bills in the AFL Championship Game, earning his team the honor of representing the AFL in Super Bowl I, the first championship game between the AFL and their NFL rivals. The NFL champion Green Bay Packers won easily, 35-10, but Dawson performed fairly well, completing 16 of 27 passes for 210 yards and one touchdown, with one interception. Dawson was selected by his peers as a "Sporting News" 1966 AFL All-League player.