DETROIT -AP- The Cleveland Indians clinched the AL Central title Monday night, overcoming an injury to ace right-hander Corey Kluber in a 7-4 victory over the Detroit Tigers.Kluber left after four innings with right groin tightness, joining Carlos Carrasco and Danny Salazar in a group of talented Cleveland pitchers dealing with injuries. But even those concerns were secondary when the Indians poured onto the field to celebrate their first division title since 2007.Cleveland last made the postseason in 2013 as a wild card.Coco Crisp and Roberto Perez homered for the Indians, and Jason Kipnisdoubled in a run.Buck Farmer (0-1) allowed four runs in five innings for the Tigers, who fell two games behind Baltimore for the second AL wild card.Andrew Miller (10-1) won in relief, and Cody Allen pitched the ninth for his 30th save in 33 chances.Crisp and Detroit's J.D. Martinez traded two-run homers in the second, and Cleveland took the lead for good in the fifth on the double by Kipnis.Mike Napoli's sacrifice fly later that inning made it 4-2.With the division title 15 outs away, the Indians took the field for the bottom of the fifth without their ace. Kluber, the team leader with 18 wins, was replaced by Dan Otero, and the announcement about the 2014 AL Cy Young Award winner's groin problem came a little while later.Miguel Cabrera made it 4-3 with an RBI single, but Perez led off the seventh with a drive to right to put the Indians back up by two.Cabrera added another run-scoring single in the seventh, but Perez -- who entered the game hitting .168 -- answered with another big hit in the eighth, lining an RBI single up the middle.Cleveland made it 7-4 on an error by Martinez in right.Miller, the third reliever for the Indians, struck out four of the six hitters he faced before giving way to Allen. The final out came on a strikeout byCameron Maybin.It was fitting that Cleveland clinched the division with a head-to-head victory over the Tigers, because that's how the Central was won. The Indians are 14-2 against Detroit with three games left in the season series.Cleveland also has been solid against other teams, of course. The Indians won 14 games in a row from June 17 to July 1, a run that coincided with the Cavaliers winning the NBA title to end the city's 52-year championship drought. The Indians are aiming to win the World Series for the first time since 1948.