Pitching for the Double-A Harrisburg Senators of the Eastern League in 2014, Purke struggled with a 1–6 record and an 8.04 ERA.

[8] He split the 2015 season between Harrisburg, Potomac, and Hagerstown, accumulating a 3-6 record and 4.36 ERA with 43 strikeouts in 64.0 innings of work between the three teams.

On November 21, 2015, Purke signed a minor league contract with the Chicago White Sox organization that included an invitation to Spring Training.

[9] He made his MLB debut on May 20, pitching an inning and a third of scoreless ball against the Kansas City Royals.

[11] Purke spent the 2017 season in Triple-A with Charlotte, and posted a 4-5 record and 3.84 ERA in 48 appearances with the team.

[14] On May 10, 2019, Purke signed with the Sugar Land Skeeters of the Atlantic League of Professional Baseball.

On March 10, 2020, Purke signed with the High Point Rockers of the Atlantic League of Professional Baseball.

On August 11, 2020, Purke announced his retirement of professional baseball and returned to his alma mater, Texas Christian University, to serve as a student assistant on the coaching staff as he completed his undergraduate degree.