Marshall won the National League Cy Young Award in 1974 as a member of the Dodgers as well as being named the NL Pitcher of the Year by The Sporting News. He set a Major League record for most appearances by a relief pitcher in 1974, appearing in 106 games. He was a member of the National League All Star Team in 1974 and 1975. Marshall was also named Fireman of the Year by TSN with three different teams: in the NL in 1973 with the Montreal Expos and 1974 with the Los Angeles Dodgers, and a third time in 1979 in the American League with the Minnesota Twins (sharing the award with Jim Kern).

Marshall, who relied primarily on an elusive screwball, led his league in games pitched four times, saves three times, and games finished five times. He is the holder of two major league records, both of which he set in the 1974 season: most appearances (games pitched) in a season (106), and most consecutive team games with a relief appearance (13). In his record-setting 1974 season, he pitched 208.3 innings, all of which came in relief appearances.