Born in Punxsutawney, Pennsylvania, Hunter was signed by the Brooklyn Dodgers in 1948. He was sold to the St. Louis Browns of the American League (AL) on October 14, 1952, for $150,000 after leading the Texas League in fielding and stolen bases. Hunter was the starting shortstop for the last Browns club in 1953 and the first modern Baltimore Orioles team when the Brownies moved to Maryland in 1954. For the remainder of his career, however, he was a second-string infielder for the New York Yankees, Kansas City Athletics and Cleveland Indians. Hunter batted .219 with 16 home runs and 144 RBI in 630 games over his six-year (1953–58) AL career.

When Hunter's playing career ended, he scouted for the Indians and Orioles. He managed the Bluefield Orioles to Appalachian League championships in 1962 and 1963. He was promoted to Baltimore on November 20, 1963 as third-base coach by former Yankees teammate Hank Bauer, who had become the team's manager one day earlier. He performed that role for almost 14 seasons for four AL champions and two World Series winners. Hunter declined an offer from former Orioles general manager Harry Dalton to manage the California Angels on November 23, 1971.

Hunter left the Orioles on June 27, 1977 to become the Texas Rangers' fourth manager that season, succeeding Connie Ryan, who had served in the interim for six games. His appointment ended the Rangers' bizarre search for a new manager, which had begun five day prior with Frank Lucchesi's dismissal, followed by Eddie Stanky's one-game stint. Despite the team trailing by 5+1⁄2 games in fifth place in the AL West, he stated upon his arrival, "I am accepting this job because I think the Texas Rangers have a contending team." Under Hunter, the Rangers won 60 of their final 93 games and climbed from fifth to second place.

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