Hauss was drafted in the ninth round (115th overall) of the 1964 NFL Draft. He started his first game at center four games into the 1964 season, a job he would not lose until retirement. Hauss helped lead the Redskins to the Super Bowl VII in 1972. He started 192 consecutive games for the Redskins between 1964 and 1977. He was named to the Pro Bowl each year between 1967 and 1972. In 1978, he was replaced by Bob Kuziel.