Dunlap played second base for the St. Louis Maroons from 1884 to 1886 and also served as the team's manager for portions of those seasons. During the 1884 season, the Maroons and Dunlap dominated the Union Association. The team compiled a record of 94-19, and Dunlap led the new league in most significant offensive and defensive categories. His .412 batting average was 56 points higher than any other player in the Union Association, the National League, or the American Association. He also led the league in on-base percentage (.448), slugging percentage (.621), runs scored (160), hits (185), total bases (279), home runs (13), extra base hits (60), assists by a second baseman (300), putouts by a second baseman (341), range factor at second base (6.41), and fielding percentage at second base (.926). Dunlap's .412 batting average in 1884 was the highest ever recorded in any of the major leagues up to that time. His 160 runs scored in 1884 remains one of the highest single-season totals in major league history.