The Athletics closed within seven games of the Rangers for first place in the American League West. Oakland needs to sweep the series to keep its slim hopes of catching the Rangers alive. A sweep would put the A's within four games of Texas with seven to play.
Braden (10-13), who threw a perfect game against Tampa Bay in May, allowed a two-out infield single to Nelson Cruz in the first and then retired 19 in a row.
The only two walks he allowed came back-to-back to open the eighth but he escaped that threat and gave way to Brad Ziegler in the ninth.
Ziegler walked a batter and hit another but protected the one-hitter.
Texas starter Cliff Lee (12-9) lasted only five innings, giving up four runs on six hits.
Lee walked the first two men he faced in the fourth and eventually gave up runs in the inning on a single by Jack Cust and a sacrifice fly by Chris Carter.
Steve Tolleson doubled in a run in the fifth and scored on a double play grounder off the bat of Daric Barton. Matt Carson doubled home the final Oakland run in the sixth.
The Rangers continued to struggle at the plate. They have scored more than two runs just twice in their last seven games.