Garza (12-7) yielded five hits and two walks to establish a career high in wins and raise his record to 3-0 in four career starts against the Rangers at Tropicana Field.
Carl Crawford homered, went 3-for-5 and drove in three runs. Evan Longoria also had three hits and three RBI for Tampa Bay, which stayed even with the New York Yankees in a first-place tie atop the American League East.
Jason Bartlett chipped in with three hits and an RBI for the victors.
Texas starter Tommy Hunter (9-2) was touched for four runs on six hits over three innings.