Baumgarten posted a win-loss record of 13–8 in 1979, and was sixth in the American League with three shutouts. He finished fourth in American League Rookie of the Year voting, and was voted to the 1979 Topps All-Star Rookie Team. On July 2, 1980, Baumgarten pitched a one-hitter for the White Sox against the California Angels. The lone Angels hit was a single by Rod Carew in the top of the seventh inning, and the White Sox won the game, 1–0.