He had a distinguished prep career at St. Louis University High School and signed his first contract with the Cardinals in 1936, but was drafted by the Pittsburgh Pirates, where his father had become minor league director, after the 1939 season.

After appearing in only 22 games for Pittsburgh between 1939 and 1941, Schultz made his way back to St. Louis with the Browns of the American League, where he spent six seasons (1943–48) as a backup catcher and pinch hitter.

Although they were badly outdrafted by their fellow expansion team, the Kansas City Royals, during the player selection lottery, Schultz and general manager Marvin Milkes actually thought the Pilots would finish third in the newly formed American League West.

The Pilots' year of existence was immortalized in Ball Four, the best-selling, controversial memoir of the 1969 season by Seattle pitcher Jim Bouton that was published in 1970.

According to Bouton, Schultz's speeches were heavily laced with profanity, even with some original curses (his favorites being the seemingly interchangeable and used for all occasions: "shitfuck" and "fuckshit").

In a May 28 game against the Baltimore Orioles, he accidentally gave the umpire the wrong lineup card, which came to backfire when opposing manager Earl Weaver noticed they were batting out of order.