As a rookie in 1963 Morehead broke into the Red Sox starting rotation and posted a 10–13 record with a 3.81 earned run average.

On May 12 of that same year, he pitched a one-hitter against the same Senators, the lone hit coming on a Chuck Hinton home run.

On September 16 of the latter year, the same day the Red Sox fired Pinky Higgins as general manager, Morehead no-hit the Cleveland Indians 2–0 before only 1,247 fans in a day game at Fenway Park, the lone baserunner coming on Rocky Colavito's second-inning walk.

Parnell's and Wilson's no-hitters, like Morehead's, had also been pitched at Fenway Park—one of Major League Baseball's most notorious hitter-friendly stadiums.

In spring training of 1971, the Royals released him; he had pitched his final game at 28 years of age, the arm ailments having ended his career prematurely.