He began his journey with the Fort Myers Miracle, but quickly showed that he was at another level than the other players in the league. Teaming with Kevin Slowey, Garza nearly led the Miracle to the first half title, as he went 5-1 with a 1.42 earned run average in eight starts. In fact, he was so dominant that hitter batted only .169 against him, and he struck out 53 in only 44.1 innings of work.
Garza made his first start for Double-A New Britain on May 18, and quickly showed that this could be just another quick stop on his tour of the Twins Minor League system. In his first outing, Garza struck out 13 batters in 7.2 innings of work, earning the win against New Hampshire. He would go on to win three of his first four starts, and finished his Double-A season with a 6-2 record him ten starts.
After tossing eight shutout innings against New Hampshire on July 5, Garza was promoted to Rochester, which would be his final Minor League stop in 2006.
Garza would make only five starts for the Red Wings once being promoted from Double-A, and he looked just as dominant as Francisco Liriano looked last season for the Wings. In his five starts, Garza compiled a 1.85 earned run average, and he won three of his last four starts. He did not allow more than three earned runs in any of his starts, and he held the opposition to a .174 batting average. He also struck out nearly a batter an inning, and after a seven inning shutout of Charlotte on August 4, a game in which he struck out 11, Garza was recalled to the Major Leagues.
Since joining the Twins, Garza has struggled at times, but he has also shown flashes of brilliance. In six starts, Garza has a 6.23 earned run average, but that is mostly due to him struggling when he was first called up. His best outing was a six inning effort against Baltimore, where the young fireballer allowed no earned runs, picking up his first Major League victory. One thing is for sure, Garza will be in the Twins rotation in 2007, and with the experience he is going to gain this season, he could be a guy that wins 15 games next season.