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 postseason in consecutive years for the first time since 1934-35.
"We wanted to win this game. That was our goal, to win this one," Cabrera said. "We did it."
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.
"It was a rocky road, it was a tough season, but in this business, you have to be able to take some hits," manager Jim Leyland said.
Now with Cabrera (.325, 44 HRs, 137 RBIs) closing in on a Triple Crown and Justin Verlander (17-8, 2.64 ERA) in contention for a second straight Cy Young Award, Detroit, winners of seven of eight, is the majors' hottest team.
Athletics 4, Rangers 3: Coco Crisp's latest clutch hit helped put Oakland back in the playoffs for the first time in six years. Crisp had a go-ahead RBI double in the fifth as Oakland (92-68) pulled within one game of Texas (93-67) in the AL West race with two to go and moved into a tie with Baltimore for the American League's top wild card.
Angels 8, Mariners 4: Mike Trout went 4-for-5 to raise his average to .325 for the host Angels, who were eliminated from the wild card when Oakland won.
White Sox 11, Indians 0: White Sox rookie Hector Santiago allowed one hit in seven shutout innings to beat host Cleveland, but Chicago was eliminated from postseason contention when Detroit defeated Kansas City.
Phillies 2, Nationals 0:Despite the loss to Philadelphia, host Washington won the NL East title, its first division title since moving from Montreal in 2005, because second-place Atlanta lost at Pittsburgh. Washington, in first since May 22, leads Atlanta by three games with two to play.
Pirates 2, Braves 1: Atlanta will be the top NL wild-card team and host the wild-card game Friday after its NL East title hopes were dashed by host Pittsburgh.
Cardinals 4, Reds 2: Jaime Garcia homered off Bronson Arroyo and pitched into the seventh inning, helping host St. Louis clinch a tie for the second NL wild card and spoil Dusty Baker's return from a mini-stroke. The defending World Series champions have won 11 of 14. The Reds (96-64) are tied with the Nationals for the best record in the NL with two games to go, and must finish ahead of Washington to get home-field advantage throughout the postseason after losing the season series.
Dodgers 3, Giants 2: Elian Herrera singled in the go-ahead run in the bottom of the ninth inning to lift the Dodgers and keep their postseason hopes alive. The Dodgers' sixth consecutive victory tied a season high and kept them two games behind St. Louis for the second NL wild card. -- AP