After being drafted by the Dodgers in 1968, Alexander debuted in the big leagues in 1971 with the team. He was traded, along with Bob O'Brien, Sergio Robles and Royle Stillman, to the Baltimore Orioles for Frank Robinson and Pete Richert in the offseason. Alexander enjoyed his first winning season with the Orioles in 1973, when he went 12–8 with a 3.86 ERA. Alexander was traded to the New York Yankees as part of a ten-player deal in the middle of the 1976 season and went 10–5 to help the Yankees win the American League East division. He did not pitch during the American League Championship Series, so he was tapped to start Game 1 of the World Series against the Cincinnati Reds, which he lost. Alexander signed with the Texas Rangers as a free agent in the offseason and enjoyed one good year before falling apart. It would not be until he signed with the Toronto Blue Jays during the 1983 season, after being released by the New York Yankees, that he would return to form.