The two-time defending American League champion Rangers (92-64) have a four-game division lead over the A's with six to play, including three games in Oakland next week. The Athletics own a two-game edge in the race for the second wild card.
Kinsler's 19th homer, his major league-best seventh leadoff shot this season, started a five-run first for the Rangers against Travis Blackley (5-4). The Rangers had four consecutive two-out hits, capped by Mike Napoli's two-run homer.
Harrison (18-10) went six innings, allowing four runs, to become the Rangers' first 18-game winner since Kenny Rogers in 2004.
Josh Reddick went deep twice, including one of Oakland's three solo homers in the eighth off reliever Mike Adams. Joe Nathan worked a perfect ninth with two strikeouts for his 36th save in 38 chances.
The Rangers are one win from clinching a playoff berth.
MARINERS 9, ANGELS 4
ANAHEIM, Calif. (AP) — John Jaso hit a two-run homer and an RBI double for Seattle, and the Los Angeles Angels wasted a chance to get within one game of an AL wild-card spot.
Vernon Wells and Alberto Callaspo drove in early runs for the Angels (86-70), who had won five straight and an AL-best 16 of 23 in September before stumbling in their regular-season home finale.
Los Angeles remained two games behind Oakland with six to play. The Angels also fell three games back of idle Baltimore, the wild-card leader.
Hisashi Iwakuma (8-5) pitched six innings of seven-hit ball, and the Mariners avoided a series sweep by scoring six runs against the Los Angeles bullpen, which held them hitless Tuesday.
Dan Haren (12-12) yielded six hits and two earned runs in 5 1-3 innings. The Angels finish the regular season at Texas and Seattle.
TIGERS 5, ROYALS 4
DETROIT (AP) — Doug Fister set an AL record by striking out nine straight batters and Detroit increased its lead in the Central, beating Kansas City on Alex Avila's grounder in the ninth inning.
The Tigers have a two-game division lead over the Chicago White Sox, who lost to Tampa Bay.
Fister came within one strikeout of matching Tom Seaver's major league record of 10 in a row. But the Tigers blew a 4-0 lead after seven innings, and Joaquin Benoit (5-3) allowed a solo homer by Billy Butler to tie it in the ninth.
The Royals made five errors, including one that loaded the bases in the ninth. Avila hit a grounder to first baseman Brayan Pena, who made a diving stop and touched the bag, but had no play at home.
Tim Collins (5-4) took the loss.
Fister finished with 10 strikeouts in 7 2-3 innings. He allowed two earned runs and five hits.
RAYS 3, WHITE SOX 2
CHICAGO (AP) — Evan Longoria hit a tie-breaking homer in the ninth inning and the surging Tampa Bay Rays won their eighth straight game, handing the White Sox a loss that hurts Chicago's playoff chances.
The Rays and Angels are two games behind Oakland in the race for the second AL wild card. The White Sox fell two games behind first-place Detroit in the AL Central after their eighth loss in nine games. Tampa Bay and Chicago have six games to go, including three more against each other.
Longoria's 14th homer came off Brett Myers (3-4) on the eve of the anniversary of his dramatic shot that beat the Yankees on the final day last season and gave the Rays the AL wild card.
Joel Peralta (2-6) pitched an inning for the win and Fernando Rodney finished for his club-record 46th save in 48 chances. After giving up a two-out single to Kevin Youkilis, Rodney struck out Adam Dunn on a 3-2 pitch to end the game.
Luke Scott also homered for Tampa Bay.
BLUE JAYS 6, YANKEES 0
TORONTO (AP) — Brandon Morrow and two relievers combined on a five-hitter, pitching Toronto to a victory that trimmed New York's tight lead in the AL East.
Edwin Encarnacion had three hits and three RBIs. Brett Lawrie hit a two-run homer and J.P. Arencibia added a solo shot as the Blue Jays handed an assist to idle Baltimore, shaving New York's division lead over the Orioles to one game.
New York lost for the third time in five games and wasted a chance to go two up with six to play.
Making his third start since missing 14 games with a sore right shoulder, Yankees right-hander Ivan Nova (12-8) allowed four runs and six hits in 4 2-3 innings.
Morrow (9-7) scattered four hits over seven innings to win for the first time in five starts. It was his longest outing since returning from the disabled list Aug. 25 after missing 65 games with a strained muscle in his left side.