Closser was selected by the Arizona Diamondbacks in the 5th round of the 1998 MLB Draft and played in their minor league system through 2001.

The Diamondbacks traded Closser and Jack Cust to the Colorado Rockies on January 2, 2002, for Mike Myers.

With the Tulsa Drillers in 2003, Closser hit .283 with 13 home runs and 54 RBI, earning a spot on the Texas League All-Star team.

He was released by the Yankees on August 6 and signed with the Portland Beavers, the Triple-A affiliate of the San Diego Padres.

With the Isotopes, Closser batted .295 with 2 homers and 31 RBI while alternating time at catcher and first base, sharing the catching duties with A. J. Ellis.