 Blevins was drafted by the Chicago Cubs in the 17th round (516th overall) of the 2004 Major League Baseball draft.He signed with the club on June 23 of that year, and began his pro career with the Single-A Boise Hawks, where he pitched 23 games, and was 6-1 with 5 saves and a 1.62 ERA, and 42 strikeouts in 33.1 innings.He was named a 2004 Northwest League mid-season All Star.