Garza, acquired July 22 from the Chicago Cubs to bolster the Rangers' rotation, is 0-2 his last four starts.
"I feel fine, just didn't have location and paid for it," Garza said. "You've got to let them go. You can't dwell on them."
Felix Pie had a leadoff walk in the third, stole second and scored on Neil Walker's single. The Pirates loaded the bases in the fourth before Barmes drew a walk, and another run came home on a fielder's choice after shortstop Elvis Andrus bobbled a likely double-play grounder.
Barmes' solo homer in the eighth that made it 7-5 was the only home run hit by either team in the series.
With his breaking ball working, Burnett struck out five the first two innings and didn't allow a base runner until A.J. Pierzynski's one-out double in the fifth.
"That's about the only time it was effective. I started to lose it toward the end," Burnett said. "My arm started dragging a little bit. But I just wanted to come out and set the tone and keep it going."
That first hit by Pierzynski might have been caught if Gold Glove center fielder Andrew McCutchen wasn't getting a day off. The ball went over the outstretched glove of Pie.
Burnett gave up five hits and walked two over the last 10 batters he faced. After the bottom two batters in the Rangers lineup walked to start the sixth, they scored when Andrus got a single that ricocheted off shortstop Barmes' glove into short left as he tried to make a backhanded stop.
Notes: Texas was 10-10 in interleague play. ... Suspended Rangers slugger Nelson Cruz started workouts Wednesday at the team's spring training complex in Arizona with full defensive drills and batting practice. Instructional league games begin next Wednesday. Cruz's 50-game suspension, through the end of the regular season, came after Major League Baseball's investigation into the Biogenesis clinic in Florida accused of distributing banned performance-enhancing drugs. Cruz could be eligible for the postseason.
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