Law made his major league debut for the Pirates in 1950. He played one season and then served in the military from 1951 to 1954. Upon returning the major leagues, eventually earned a spot in the Pirates' starting rotation, steadily demonstrating solid pitching abilities. In 1960, he had a win–loss record of 20-9 with a 3.08 earned run average. He led the National League in complete games, made the all-star team, and won the Cy Young Award that season. In the 1960 World Series, he won two games to help the Pirates defeat the New York Yankees.

This Rawlings official MLB baseball was signed in blue by Law and inscribed, "Cy Young 1960." This baseball includes a Steiner hologram and COA as well as an MLB hologram.