Optimistically nicknamed "Win", Kellum became the first Opening Day starting pitcher in the Boston American League franchise's history, as they lost to the host Baltimore Orioles, 10–6, at Oriole Park (April 26, 1901). He went 2–3 with a 6.38 ERA for the rest of the season.
Kellum rebounded in 1902, going 25–10 with the minor leagueIndianapolis Indians, champions of the newly formed American Association. After the regular season, he pitched with barnstormers largely made up of Cincinnati National League team. After that, he enjoyed his best season in the majors with the 1904 Reds, going 15–10 while recording career-highs in ERA (2.60), complete games (22) and innings (224). He also pitched for the Cardinals in 1905, his last major league season, and went 3–3 with a 2.92 ERA.
In a three-season career, Kellum posted a 20–16 record with a 3.01 ERA in 48 appearances, including 37 starts, 32 complete games, two shutouts, two saves, 97 strikeouts, 63 walks, and 346+2⁄3 of work.