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 One 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. The Blue Jays were on the rise in the mid 1980s, and Alexander was an instrumental part of their success, winning 17 games in both 1984 and 1985, including the division-clinching win over the Yankees in 1985. In the ALCS, however, he went 0–1 with an 8.71 earned run average in two starts as the Blue Jays fell to the Kansas City Royals in seven games. When Alexander negotiated his contract with the Blue Jays, the team refused to pay Alexander if he injured himself while hunting. Toronto lawyer Gord Kirke worked out a compromise in which Alexander would collect money while hurt, "only if he was following all hunting regulations and wearing an orange hunting jacket". A slow start the next year resulted in Alexander being traded to the Atlanta Braves, who dealt him in turn to the contending Detroit Tigers midway through the 1987 season for a then unknown minor-leaguer named John Smoltz. The Tigers got more than they could have possibly hoped for in Alexander, who went 9–0 with a 1.53 ERA to propel the Tigers to the division title. However, he struggled again in the ALCS, going 0–2 with a 10.00 ERA, bringing his postseason totals to 0–5 with an 8.38 ERA. The following year, Alexander went 14–11 with a 4.32 ERA, earning his only All-Star appearance. In 1989, his performance declined in part due to pitching with a fractured jaw. He retired following the season.
