Law signed for the Pirates as an amateur free agent in 1948 and played for three of their minor league affiliates until 1950, when he was promoted to the major leagues.
Law was born on March 12, 1930 in Meridian, Idaho. He was signed by the Pittsburgh Pirates before the 1948 season and spent 1948 and 1949 in the minor leagues.
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. He shared the NL Player of the Month award in August 1959 (4-0, 1.94 ERA, 25 SO) with Willie McCovey.
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.
His career was derailed by an injury to his ankle sustained on the bus trip on which the team was celebrating clinching the 1960 pennant. Law was forced to change his pitching style and pitched in pain for the rest of the season and the World Series. Because of his weak ankle, he tore some muscles in the back of his pitching shoulder during the Series. He thought the injury would heal over the winter, but he was not the same for several seasons.
He did manage to win the NL Comeback Player of the Year award in 1965, with a 17-9 record, and a 2.15 ERA in 29 games. He shared the NL Player of the Month award in June of that year (with Willie Stargell), with a 6-1 record, 0.87 ERA, and 32 SO. After two more seasons, he retired in 1967.
Law finished his career with a record of 162-147. He won the Lou Gehrig Memorial Award in 1965 for his contributions both on and off the field.
Law was made a deacon in The Church of Jesus Christ of Latter-day Saints at the age of 12, became a teacher two years later and was ordained a priest at 17. During his playing career, Law was tagged with the nickname "Deacon" by Pirate broadcaster Bob Prince. According to Law, it was given to him by former Pirate teammate Wally Westlake because he is a member of the ordained priesthood of the LDS Church.
Law was the pitching coach for the Provo High School (PHS) varsity baseball team and is an active member of The Church of Jesus Christ of Latter-day Saints. He currently lives in Provo, Utah.
Law has been credited with saying, "A winner never quits and a quitter never wins" and "Experience is a hard teacher because she gives the test first, the lesson afterwards."
His son Vance Law also played in the major leagues.