Triple Crown candidate Miguel Cabrera was robbed of a tiebreaking homer in the fifth inning by Alex Gordon's catch above the left-field wall. Detroit, which started the day tied with the Chicago White Sox atop the AL Central for the first time since Sept. 2, found a way to break through the eighth, though.
It looked as if the Royals were going to keep the score tied in the eighth when Peralta hit a grounder to third baseman Mike Moustakas. Dirks, though, slid so late and hard that second baseman Irving Falu didn't attempt a throw, allowing pinch-runner Don Kelly to score.
Dirks was swarmed by teammates in the dugout to celebrate the gritty, clean play he made.
Delmon Young hit an infield single with one out in the eighth off Kelvin Herrera (4-3) and was replaced by Kelly, who stole second base and took third on Andy Dirks' single.
Alex Avila hit a two-run homer and Austin Jackson had a solo shot in the fourth inning to tie the game.
Cabrera, who went 0 for 4, started the day with the AL lead in batting average and RBIs and was one homer behind Texas' Josh Hamilton. Baseball hasn't had a player lead a league in all three categories since Boston's Carl Yastrzemski in 1967.
The Tigers have won six of nine games on their final 10-game homestand and 32 of their last 43 games at Comerica Park. They had, however, lost 11 straight one-run games since beating Toronto 3-2 on Aug. 23.
Kansas City has lost four straight since winning four in a row, including two against the White Sox.
Detroit starter Rick Porcello lasted just four innings, giving up four runs and seven hits.
Luis Marte got two outs in the fifth and Al Alburquerque gave up only one hit over 2 1-3 innings. Joaquin Benoit (4-3) allowed one hit in the eighth. Jose Valverde closed the game for his 32nd save in 37 chances.
Royals starter Jeremy Guthrie allowed four runs on seven hits and two walks over seven innings.
Young doubled and Dirks singled to give the Tigers a 1-0 lead in the second.
Kansas City went ahead 3-1 in the third inning after Falu, David Lough and Billy Butler doubled. Jeff Francoeur's solo homer in the fourth inning gave the Royals a three-run lead.
NOTES: Detroit is sending Doug Fister (10-9) to the mound in its final scheduled home game Thursday afternoon against Kansas City and Luis Mendoza (8-9) before the Tigers close the regular season on the road against Minnesota and the Royals. ... Guthrie was 4-0 with a 1.75 ERA in his previous nine starts all of which were Kansas City wins. ... Porcello is 0-6 in his last eight outings. ... Yastrzemski told reporters in Boston on Wednesday that playing meaningful games down the stretch with help Cabrera's attempt to win the Triple Crown. "One thing that's going to help him is he's in a pennant race," Yastrzemski said.
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