After graduation from Central College in Pella, Iowa, in 1950, Schultz began his coaching career at Humboldt High School in Humboldt, Iowa. He turned down a chance to play baseball for the St. Louis Browns organization in order to teach and coach. Over a ten-year period, Schultz taught biology and served as an assistant football, and head baseball and basketball coach.
In 1960, Schultz was hired as an assistant baseball and men's basketball coach at The University of Iowa. Schultz had a 129-106 record in 71/2 seasons as baseball coach. In 1970, when Ralph Miller abruptly left the Iowa basketball program for Oregon State, Schultz was made the men's head basketball coach. Schultz had a 41-55 mark in four seasons as Iowa's basketball coach before being replaced by Lute Olson.
From 1976 to 1981, Schultz was athletic director at Cornell University, where he hired a new football coach (Bob Blackman) and worked toward financial self-sufficiency for his department. Schultz became the athletic director at the University of Virginia in 1981 and held that position until 1987.
In 1987, he succeeded Walter Byers to became the second executive director of the NCAA.
During his five-year tenure he helped to strengthened the organization's integrity and reform by opening lines of communication with member colleges. In 1993, irregularities were discovered at the University of Virginia, some that occurred when he served as athletic director. Although cleared of all charges and receiving a vote of confidence from the membership board, Schultz thought it was appropriate to resign.