Born in Gordon, Kansas, he was signed by the Yankees as an amateur free agent out of Capitol Hill High School in Oklahoma City, Oklahoma in May, 1948. He started his professional career in the minor leagues. In 1952, he was 3-3 with a 3.56 ERA for Beaumont in the Texas League. In ‘53, he was 10-7 with a 3.76 ERA for Birmingham of the Eastern League. In ‘54, he was 8-9 with a 3.57 ERA, 133 strikeouts and just 59 walks in 169 innings for Kansas City of the American Association.
Sturdivant made his major league debut the following year, working exclusively out of the bullpen during the regular season and the third and fourth games of the 1955 World Series. He was a sixteen-game winner in each of the next two campaigns, starting a World Series game in each year, and pitching a complete game to defeat the Brooklyn Dodgers 6-2 in Game 4 of the 1956 World Series (the game before Don Larsen's perfect game). In 1957, his 16-6 record led the American League in won-lost percentage (.727), and his 2.54 ERA was second in the league.
A rotator cuff injury in 1958 greatly limited his effectiveness for the remainder of his baseball career. On May 26, 1959, he, along with Johnny Kucks and Jerry Lumpe, was sent to Kansas City for Héctor López and Ralph Terry. Sturdivant wore uniform number 32 for the A's that year.
On December 3, 1959, he was traded by the Athletics to the Red Sox for Pete Daley. He wore uniform number 15 for the Red Sox.
On December 14, 1960, he was drafted by the Senators from the Red Sox in the 1960 expansion draft. Initially he wore uniform number 35 for the Senators, but later was given the same number 47 which he had worn for the Yankees. He won the first shutout game in Senators history, a 4-0 victory over the Boston Red Sox on May 13, 1961.
On June 29, 1961, he was traded by the Senators to the Pirates for Tom Cheney. He wore uniform number 15 for the Pirates, the same number he had worn on the Red Sox.
On May 4, 1963, he was purchased by the Tigers from the Pirates. He wore uniform number 22 for the Tigers.
On July 23, 1963, he was purchased by the Athletics from the Tigers. He wore uniform number 18 for the A's this time.
After he was released by the Athletics on May 10, 1964, he signed as a free agent with the Mets later that day. He wore uniform number 47, his old Yankees number, for the Mets. He was released by the Mets on June 27.
After his retirement from the sport, he was involved in the freight and truck leasing business, concentrating on the former during the 1980s. He was once part-owner of R&R Trucking, Inc. He later served on the board of directors of Metro Tech in Oklahoma City and the Integris Hospice of Oklahoma County.
Sturdivant died on February 28, 2009, in Oklahoma City, Oklahoma.