Athletics manager Bob Geren enjoyed watching his team's rare power surge.
"Adam is such an excellent player," Geren said. "He can figure when to dial it up. That's a sign of a good, experienced player."
Scott Hairston, Kurt Suzuki and Cliff Pennington also homered for the A's, who won their third straight over the Rangers. Rajai Davis added two hits.
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"That's something we haven't done," Geren said. "It's been awhile since we've done that. Home runs are always good."
The four home runs gives the A's 86 for the season, still the fewest in the AL. The Rangers lead the majors with 161 homers.
David Murphy hit a pair of homers for the Rangers, who have lost four of their last five games.
Craig Breslow (5-5) pitched an inning in relief of A's emergency starter Chad Reineke to record the win. Andrew Bailey got three outs for his 15th save. He's converted 10 successive chances.
"There's a lot I would have liked to change, but you like to leave with the team ahead, so I'm glad I was able to do that," Reineke said. "I could have stayed in there, but they made their decision, and that was fine."
Vicente Padilla (8-6) allowed six runs on seven hits over 5 2-3 innings. He walked two and struck out four.
"He could have been better and I'm sure he'd say that. But he battled and kept us in the game," Rangers manager Ron Washington said. "It was the long ball that beat us."
Reineke was recalled from Triple-A Sacramento to replace scheduled starter Dallas Braden, who had a swollen left ankle, which developed from a rash caused by a Neoprene guard used to protect his big toe when pitching.
"I got my debut out of the way last year, so I wasn't that nervous," Reineke said. "I was a little anxious, but the worst was the two hours leading up to the game."
He became the 11th starter used by the A's and the sixth consecutive rookie starter, matching an Oakland record. Reineke appeared in a handful of games with the San Diego Padres last year.
"The guy doesn't have a whole lot of velocity but he competed and threw the ball over the plate," Washington said.
Taylor Teagarden and Josh Hamilton also drove in runs for the Rangers. Hamilton's sacrifice fly in the sixth tied it 5-all.
"We know we're a good team," the Rangers' Michael Young said. "We're not going to let a couple bad games ruin what we've built up so far this year. We'll make our adjustments. We always do."
Padilla allowed a one-out double to Mark Ellis and then struck out Pennington before giving way to Neftali Feliz, who allowed Kennedy's home run.
NOTES: OF Eric Patterson was optioned to Sacramento (PCL) to make room for Reineke. ... The Rangers recalled IF Esteban German from Triple-A Oklahoma City and optioned IF Joaquin Arias. ... Rangers RHP John Bannister was designated for assignment. .. The A's doubled twice and have a major league-best 52 doubles since the All-Star break. ... The Rangers are 1-7 in games played in the San Francisco Bay Area. ... Young singled in the first to extend his hitting streak to 12 games.