The A's won for the third straight night in a four-game series that concludes Thursday.
Texas overcame a two-run deficit to take a 3-2 lead, and then rallied from two runs down again to forge a 5-5 tie going into the bottom of the sixth.
Vicente Padilla (8-6) gave up a one-out double to Mark Ellis in the sixth, but after retiring Cliff Pennington on strikes was relieved by Neftali Feliz.
Feliz, who struck out the first four batters he faced in his major league debut Monday, served up the home run pitch to Kennedy on a 1-0 count.
The win went to Craig Breslow (5-5), even though he gave up the tying run in the top of the sixth on a sacrifice fly by Josh Hamilton. Andrew Bailey worked a perfect ninth for his 19th save.
David Murphy hit two home runs for Texas while Kurt Suzuki and Pennington hit solo shots for the Athletics.
Texas remained 4 ½ games behind division-leading Los Angeles in the American League West. The Rangers and Angels begin a three-game series in Anaheim Friday.
Copyright 2009 by United Press International.