Woodeshick spent most of his career as a relief pitcher and had his best seasons in that role. After going 5-16 for the expansion Colt .45s (later the Astros) in 1962, mostly as a starter, he was used exclusively out of the bullpen and had his three best years. He had a 1.97 ERA in 1963 and a league-leading 23 saves in 1964. St. Louis acquired him in June 1965 with Chuck Taylor in exchange for Mike Cuellar and Ron Taylor, but Woodeshick was behind Joe Hoerner and Nellie Briles in the Cardinals bullpen and saw less crucial action thereafter. In Game Six of the 1967 World Series, he was the eighth Cardinals pitcher in the game, tying a record.