The Connecticut-born reliever was drafted by the Reds and then traded in 1983 to Houston for catcher Alan Knicely. In three years with the Astros, Dawley posted a 22-13 record with a 2.71 ERA and 21 saves. Dawley was a surprise choice for the 1983 All-Star team where he gave up one hit and no runs in 1-1/3rd innings.

Cut by the Astros during the 1986 season, Dawley pitched for the White Sox, Cardinals, Phillies and Athletics before retiring.