Dobson signed with Detroit in 1959. After spent seven years in the minors and in winter ball, pitching mostly in relief, he made his debut with the big team in the 1967 season. Dobson was traded to San Diego in 1969 and attracted the attention of the Orioles after going 14-15, with 185 strikeouts and a 3.76 of earned run average, as the ace staff for the 1970 last-place Padres.

In 1971 Dobson had a winning streak of 12 games (nine consecutives) and a scoreless inning streak of 23. That September 24, he reached his 20th win; a 7-0 shutout against the Cleveland Indians. Dobson posted a 20-8, 187, 2.90 season record, and was part of the Orioles' "The Big Four" pitching staff along with Dave McNally (21-5), Mike Cuellar (20-9) and Jim Palmer (20-10). Baltimore went on to win 101 games and having the honor to have four 20-game winners in a season. Only one other team in MLB history, the 1920 Chicago White Sox, have had four 20-game winners.

On November 2, 1971 the Orioles' Dobson threw a 2-0 no-hitter against the Yomiuri Giants at Tokyo. It is the first no-hitter game in the Japanese-American baseball exhibition history.

Dobson was an All-Star in 1972. His 2.65 ERA was a major improvement from his 20-win season, but he went 16-18, tying the AL lead in losses. After the season, he was traded to the Braves along with Davey Johnson. Dobson was then sent to the Yankees in mid-1973. The next year he went 19-15 with a 3.07 ERA, turning in the best New York pitcher. After a slumping 11-14, 4.07 in 1975, Dobson was traded to the Indians and recovered with a 16-12, 3.48 . After his 3-12, 6.16 record in 1977, he finished his career.

In his 11-season career Dobson had a record of 122-129, with 1301 strikeouts, a 3.54 of earned run average, 74 complete games, 14 shutouts, 19 saves, and 2120 innings pitched in 414 games.