Gerald Laird added a bases-loaded double, Rick Porcello (10-12) pitched shutout ball into the sixth inning and Jhonny Peralta went deep off Bruce Chen (11-14) to help Detroit reach the post-season in consecutive years for the first time since 1934-35.
After hanging over the dugout railing the entire ninth inning, the Tigers streamed onto the field and behind the pitchers' mound to celebrate their accomplishment the moment Jose Valverde got Alcides Escobar to ground out to shortstop with a runner on second for his 35th save in 40 chances.
The Tigers (87-73) will have the worst record among AL division champions, which means they'll open the playoffs Saturday at home against the division winner with the second-best mark.
Cabrera, making a run at baseball's first Triple Crown since 1967, broke a tie with Texas slugger Josh Hamilton for the major league lead in homers with his 44th, a solo shot to right.
Prince Fielder also had four hits.
ATHLETICS 4, RANGERS 3
OAKLAND, Calif. (AP) — Coco Crisp's latest big hit helped put Oakland back in the playoffs for the first time in six years, and the Athletics beat first-place Texas to remain in contention for a division crown.
Crisp had a go-ahead double in the fifth inning as the A's (92-68) pulled within one game of Texas (93-67) in the AL West with two to go and moved into a tie with Baltimore for the American League's top wild card.
Oakland's victory eliminated the Angels and Rays from post-season contention.
Pinch-hitter Brandon Moss delivered a sacrifice fly for insurance and Josh Reddick added an RBI single for the resurgent A's, who must sweep this season-ending series against the two-time reigning AL champions to capture the West title.
Michael Young and Mike Napoli homered against Jarrod Parker (13-8), who is 3-0 against the Rangers this year.
Grant Balfour struck out the side for his 23rd save, giving the young A's their fourth straight victory and sixth in seven games.
Martin Perez (1-4), facing the A's for the third time in his six major league starts, lasted four-plus innings.
YANKEES 10, RED SOX 2
NEW YORK (AP) — Robinson Cano, Curtis Granderson, Russell Martin and Mark Teixeira homered in a nine-run second inning, and New York routed Boston to open a one-game lead over Baltimore in the AL East with two games to play.
Baltimore lost at Tampa Bay and dropped into second place, prompting cheers from the Yankee Stadium crowd when the final score was posted before the ninth inning. The Yankees, who clinched their 17th playoff berth in 18 years on Sunday, would ensure their 13th division title in 17 years by sweeping the three-game series against the Red Sox.
New York tied its record for home runs in an inning, achieving the feat for the third time. The offence backed CC Sabathia (15-6), who allowed two runs and four hits in eight innings with seven strikeouts.
Alex Rodriguez hit a sacrifice fly to end a streak of 11 games without an RBI. He tied Stan Musial for fifth place on the career list at 1,950.
Boston, starting what may be its final series under first-year manager Bobby Valentine, has lost six in a row and 10 of 11, reaching 91 defeats for the first time since dropping 100 games in 1965. The Red Sox started just two regular position players, Cody Ross and Jarrod Saltalamacchia.
Clay Buchholz (11-8) was roughed up for a career-high eight runs and six hits — three of them homers — in 1 2-3 innings.
RAYS 5, ORIOLES 3
ST. PETERSBURG, Fla. (AP) — Alex Cobb allowed two hits over seven innings, helping Tampa Bay keep its slim playoff hopes alive with a victory over Baltimore.
Ben Zobrist hit his 20th homer and Chris Giminez had a two-run double off Wei-Yin Chen (12-11) as the Rays pulled away from a 1-all tie in the seventh. Cobb (11-9) yielded a fourth-inning single to J.J. Hardy and a solo homer to Matt Wieters that tied it in the seventh.
The Rays won for the 11th time in 12 games, a stretch that's kept them in contention for the second AL wild card. They began the night trailing Oakland by three games and must sweep the Orioles and hope the A's drop three straight to Texas.
Baltimore already is assured of being in the playoffs for the first time in 15 years.
Chris Davis homered for the fifth straight game for the Orioles, a two-run shot off Kyle Farnsworth that trimmed Baltimore's deficit to 5-3 in the ninth.
Fernando Rodney worked out of a jam to earn his 47th save in 49 opportunities.
The Orioles arrived in St. Petersburg for the season-ending series later than expected Sunday night after their plane had to divert to Jacksonville because of a fire in the galley.
ANGELS 8, MARINERS 4
SEATTLE (AP) — Mike Trout had four hits and drove in three runs against Seattle, but it wasn't enough to keep Los Angeles in the playoff chase.
The Angels, with a high payroll and high expectations when the season started, were eliminated from the wild-card race when Oakland beat Texas.
C.J. Wilson (13-10) went 6 1-3 innings for the victory. He allowed six hits and two runs, striking out seven and walking five.
Felix Hernandez (13-9) gave up a season-high 12 hits and seven runs in 5 1-3 innings. He went 0-4 with a 6.62 ERA after Aug. 27.
Trout was a home run shy of the cycle and raised his batting average to .325, four points behind Detroit slugger Miguel Cabrera for the AL lead.
WHITE SOX 11, INDIANS 0
CLEVELAND (AP) — White Sox rookie Hector Santiago allowed one hit in seven shutout innings to beat Cleveland, but Chicago was eliminated from post-season contention when Detroit defeated Kansas City.
Santiago (4-1), who began the season as the team's closer, struck out a season-high 10. The Indians' only hit off the left-hander was Shin-Soo Choo's two-out single in the third.
The second-place White Sox won for the third time in 13 games. They collapsed down the stretch after leading the AL Central for 63 straight days.
The White Sox scored four runs in the sixth off Corey Kluber (2-5) and added six in the ninth. Dayan Viciedo hit his first grand slam to make it 11-0.
BLUE JAYS 6, TWINS 5, 10 INNINGS
TORONTO (AP) — Anthony Gose singled home the winning run in the 10th inning and Toronto rallied to beat Minnesota.
Adam Lind went 4 for 4 and Brandon Lyon (4-0) worked out of a bases-loaded jam to earn the win in front of a season-low crowd of 12,359.
Adeiny Hechavarria hit a one-out single off Brian Duensing (4-12) and moved to second on a wild pitch.
Toronto tied it in the ninth when Yan Gomes hit a two-out homer, snapping Glen Perkins' streak of 12 straight successful save conversions.
Trevor Plouffe homered and had three RBIs for the Twins.
Three-time AL batting champion Joe Mauer went 1 for 5, dropping his average to .322, seven points behind Miguel Cabrera.