With the Rays, Garza was named the American League Championship Series Most Valuable Player in 2008, and threw a no-hitter on July 26, 2010.

[1] After struggling his first two years at Fresno State, Garza excelled in his junior season, averaging 10 strikeouts per nine innings pitched.

[6] Garza is one of a small number of players to advance through the minors and reach the major league level in a single season.

On August 11, his major league debut, Garza allowed seven earned runs in 2+2⁄3 innings to the Toronto Blue Jays.

[11] He was selected to the 2007 All-Star Futures Game in San Francisco, but did not get to participate due to his call up to the major league club.

Garza was put in the eight-spot when catcher Mike Redmond left the game after his head was cut by Jim Thome's bat on a backswing.

As of the end of July 2009, opposing batters were hitting .222 against him, which was the second-lowest batting average in the league; he was just behind Edwin Jackson (.216), and was followed by Jarrod Washburn (.224) and Scott Feldman (.228; .217 as a starter).

[15][16] He faced the minimum 27 batters as the lone base runner, Brennan Boesch, who drew a 1-out second inning walk, was erased on a double play hit by Ryan Raburn in the next at-bat.

[22] On July 22, 2013, The Cubs traded Garza to the Texas Rangers in exchange for Mike Olt, Justin Grimm, C. J. Edwards, and Neil Ramirez.

He attempted to pitch the rest of the season through it, but struggled badly down the stretch and lost his spot in the rotation, finishing the final year of his contract with a 6–9 record and a 4.94 ERA.

On January 10, 2018, Garza, now a free agent, underwent surgery to repair the labrum, performed by Dr. Neal ElAttrache, and was ruled out for the entire 2018 season.

His arsenal also includes a big, breaking curveball that he throws for 72–77 mph, a hard, tight slider in the mid 80s, and an occasional changeup he uses to fool hitters, especially lefties.