On July 28, 2005, together with Scott Feldman and Steve Karsay, he threw a perfect game against the Corpus Christi Hooks.

It was the first combined nine-inning perfect game in Texas League history, and the third overall.

On December 15, 2009, Murray signed a minor league contract with the Milwaukee Brewers and also received an invitation to Spring Training.

He was assigned to the Triple-A Nashville Sounds for the 2010 season, but was released on June 22, 2010.

Murray signed with the York Revolution of the independent Atlantic League on July 19, 2010.