The Pro Football Hall of Fame states that Dawson is among the elite in Pro quarterbacks with an 82.56 QB rating over a span of 19 seasons in the NFL.

He was the top pick of the Pittsburgh Steelers in 1957's NFL Draft. He served as a backup there and, later, in Cleveland until in 1962, he found his way onto the AFL's Dallas Texans roster. After the move to Kansas City and rebranding the team as the Chiefs, Dawson cemented himself as the starter.

He was named Most Valuable Player (MVP) in 1962 and was selected to play six AFL All-Star games. Dawson also guided the Chiefs to three AFL championships and the franchise's first Super Bowl title in Super Bowl IV, of which he was named MVP. The Chiefs revered Number 16 may be best remembered for his gritty performance as he led Kansas City to a 23-7 upset over the Minnesota Vikings in Super Bowl IV. In that game, Dawson connected on 12 of 17 passes for 142 yards.