They can now wrap up another division title at home even before having to face the chasing Athletics again next week in Oakland.
Kinsler hit a leadoff homer to start a five-run first inning, Matt Harrison got his 18th victory and the two-time defending American League champions held on for a 9-7 victory Thursday. By splitting the four-game series, the Rangers maintained their four-game division lead over the A's with six to play.
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"Never doubted it," manager Ron Washington said of his team's response after losing consecutive games at home. "The worse we were looking for was a split. They can also play, and we got what we wanted."
The Rangers' magic number for clinching was three heading into a weekend series at home against the Los Angeles Angels, starting Friday.
That came after the A's (88-68) had their own five-run first inning in a 9-3 win Wednesday night, after winning in 10 innings the night before that.
Texas (92-64) scored in each of the first four innings against three different pitchers, matching Oakland run-for-run in the second through the fourth until the A's hit three solo homers in the eighth off Mike Adams.
"We constantly kept the momentum in our favor, if you don't look at the three home runs in the eighth. We responded to them," Kinsler said. "We want to be a team that's tough to put away."
Josh Reddick homered twice for the A's, who wrapped up a 20-game stretch of six series in six cities and won 12 times. They finish the regular season at home, with a three-game weekend series against Seattle before hosting the Rangers starting Monday night.
""We don't have any negative thoughts right now," Reddick said. "It's going to be good to go home. We've been on the road for a month. ... We can't rely on LA to lose and we can't rely on Texas to fall back. We know we're just not going to back down."
The A's, whose 51-26 record since the start of July is best in the majors, are 2 games ahead of Los Angeles for the AL's second wild card. The Angels lost to at home against Seattle.
Harrison (18-10) went six innings, allowing four runs and seven hits, to become the Rangers' first 18-game winner since Kenny Rogers in 2004.
The All-Star left-hander is scheduled to start once more in the regular season, with a chance for the most wins since Rick Helling's 20 in 1998.
"Matt wasn't at his best, but he was able to fight through a lot of things and he was able to make pitches when he had to," Washington said.
"It was a battle for me all day," Harrison said. "All credit goes to the offense. They scored nine runs, kept us on top of the game."
Joe Nathan worked a perfect ninth with two strikeouts for his 36th save in 38 chances.
Blackley lasted only one inning, allowing five runs and five hits with a wild pitch.
"I felt pretty good when I threw in the bullpen before the game. When I get out there, the ball is just not going where I want it," Blackley said. "I'm just not getting it down. I'm not throwing my off-speed pitches for strikes and falling behind. Even when my pitches did get down, they found holes."
Kinsler extended his own franchise record with his 27th career leadoff homer. Adrian Beltre, Nelson Cruz and Michael Young then had two-out singles before Napoli's opposite-field homer to right-center.
Josh Hamilton got his 125th RBI with a double in the Texas second, an inning before Napoli's run-scoring single made it 7-2.
Reddick, who snapped a season-worst 0-for-30 slump with singles in his last two at-bats Wednesday night, made it three hits in a row when he pulled a pitch into the second deck of seats in right field in the second inning for his 30th homer of the season.
"We didn't look good early. But to battle back like that, we would have had a chance to tie the game if we got a runner on base in the ninth," A's manager Bob Melvin said. "That's testament to how good they played."
- Texas and Oakland have split their 16 games this season.
- A's rookie A.J. Griffin (6-1) starts the series opener against Seattle.
- Ryan Dempster, 7-2 for Texas since being acquired from the Chicago Cubs on July 31, starts against Angels ace Jered Weaver (19-4).
- Oakland batters struck out seven times, extending the American League season record the A's set Wednesday night to 1,340 with six games to play.
- Napoli was 0 for 11 with six strikeouts in the series before his homer.