After two 18-win seasons in 1950 and 1951, and a 12–12 record in 1952, Parnell went 21–8 in 1953 with a 3.06 ERA and a career-high 136 strikeouts. On July 14, 1956, he no-hit the Chicago White Sox, 4–0, at Fenway Park. The no-hitter was the first for a Red Sox pitcher since Howard Ehmke in 1923, though this would prove the final highlight of Parnell's career, which would come to a premature end after the 1956 season, due to a torn muscle in his pitching arm. It would take 52 years until another Red Sox lefty would throw a no-hitter, a feat accomplished by Jon Lester in 2008.
Parnell still holds the Red Sox career mark for left-handed pitchers in games started, innings and victories.
