Schulz started out as a right half back in the late 1950s. With the change from the WM system to the 4–2–4, Schulz was converted from half back to stopper by the mid-1960s. During the 1966 World Cup, Schulz acted as the sweeper of the West German national team, a role he had taken over from Klaus-Dieter Sieloff only shortly before the tournament. At that tournament, Schulz was rated as one of the best defenders. During the next four years, Schulz remained the standard sweeper of West Germany. During this time, Schulz was acknowledged as one of the best central defenders in global football. In November 1968, he was part of the FIFA XI that faced Brazil in Rio de Janeiro.