DETROIT -- With another big late-inning home run, the Detroit Tigers reopened a 1 1/2-game AL Central lead
"It's not easy to get to that guy," Kinsler said.
A night earlier, Alex Avila hit a two-out, two-run homer off Shaw in the eighth inning of the Tigers' 5-4 win.
Detroit widened its lead in the eighth inning Sunday on C.C. Lee's run-scoring wild pitch over a shoulder of catcher Chris Gimenez during an intentional walk to Kinsler. Torii Hunter followed with a run-scoring forceout.
"That was absolutely a huge play," Cleveland manager Terry Francona said of the wild pitch.
Phil Coke (5-2) pitched a scoreless seventh for Detroit, which won for the sixth time in seven games. The Tigers have their largest lead since before play on Aug. 10.
Joe Nathan gave up Carlos Santana's RBI double in the ninth before getting his 32nd save in 38 chances and eighth in a row. With runners on first and second and no outs, Yan Gomes grounded into a double play, and pinch-hitter Jason Giambi hit a game-ending flyout.
While the Tigers go to last-place Minnesota for a three-game series, second-place Kansas City hosts the Chicago White Sox for three games. Detroit plays three games at Kansas City next weekend.
"Every game is huge," Tigers manager Brad Ausmus said. "Every game we play matters. Every game Kansas City plays matters."
Detroit starter Justin Verlander allowed three runs and six hits in 5 2/3 innings, leaving his season ERA at 4.81. He is 7-8 with a 5.40 ERA since late May.
Cleveland's Trevor Bauer gave up two runs -- one earned -- and six hits in five innings. The Indians are five games back for the AL's second wild card with 14 games left.
"Now we're going to have to get real hot real fast," center fielder Michael Bourn said. "I feel like we had a chance to win two out of three. They showed us why they won the division the last three years."
J.D. Martinez hit a solo homer in the fourth, a booming drive into the center-field hedges for his 22nd home run this season.
"You don't see many guys reach the bushes out there," Ausmus said. "In terms of raw power, he's up there with anyone in the major leagues."
Santana's sacrifice fly tied the score in the fifth, and Blaine Hardy relieved Verlander with two on in the sixth. Jose Ramirez singled in the go-ahead run, and Hardy hit Michael Brantley with a pitch with the bases loaded.
Martinez pulled the Tigers to 3-2 with an RBI single in the bottom half.
Seven of Martinez's 22 homers this season have come against the Indians, and he's hit .328 with 11 runs and 20 RBIs in 16 games vs. Cleveland. Thirteen of Martinez's long balls have come against the AL Central.
CATCH OF THE DAY
A woman standing near one of the entrances to the lower deck and holding a small child managed to snag a foul ball on a hop. She crouched down as the ball bounced her way, grabbed it with her free hand. Child in tow, she resumed walking to her seats behind Detroit's dugout.
Tigers: Avila left at the end of the seventh because of what the team called lightheadedness. Ausmus said he wasn't sure whether the headache was related to a ball that struck Avila's mask earlier in the game and said he doesn't expect Avila to play Monday. Avila went 1 for 3 with a pair of strikeouts.
Indians: OF Ryan Raburn didn't play, a day after leaving a game with a hyperextended left knee. Francona said the team will evaluate Raburn before deciding whether he needs an MRI. Raburn has played just 74 games this season due to injuries.