Dunlap played for the Cleveland Blues from 1880 to 1883, where he secured his reputation as one of the best players in the game. As a rookie in 1880, he led the National League in doubles and ranked second in extra base hits. While playing for Cleveland, he also compiled batting averages of .325 and .326 in 1881 and 1883 and led the league in assists by a second baseman and range factor. When the Union Association was formed in 1884, Dunlap was lured to play for the St. Louis Maroons where he became the highest paid player in baseball. His .412 batting average in 1884 was the highest ever recorded to that time in Major League Baseball and 56 points higher than any other player in the major leagues in 1884 due to the lack of talent in the UA.