Gatorade? Water? This is Kansas City, buddy. So Eric Hosmer got a barbecue sauce shower Wednesday afternoon after delivering a walk-off RBI single that produced a pulsating 3-2 victory over the Detroit Tigers in 10 innings at Kauffman Stadium. Hosmer’s single capped a remarkable comeback that included Lorenzo Cain’s two-out homer on an 0-2 count with two outs in the ninth inning against Jose Valverde. Better late than...well, this was pretty much as good as it gets. Miguel Tejada started the winning rally with a single up the middle against Phil Coke. A sacrifice by Alcides Escobar moved Tejada to second. Coke, 0-4, fell behind Alex Gordon 3-0, fought back to a full count and retired him on a grounder to first that moved Tejada to third. Hosmer drove a clean single up the middle for the victory. The celebratory scrum surrounded Hosmer between first and second base, and he emerged with a face full of sauce. Greg Holland, 2-1, got the victory after pitching a scoreless 10th inning. Hosmer got the game-winner, but Cain’s homer might rank as the Royals’ biggest hit of the year. It not only erased a 2-0 deficit but also an afternoon of depressing offensive malaise. The homer snatched a victory away from Justin Verlander, who worked seven scoreless innings, and prevented James Shields from absorbing another tough-luck loss. Hosmer opened the ninth with a single through the left side against Drew Smyly, who had worked a scoreless eighth inning after replacing Verlander. That brought Valverde into the game. He retired Salvy Perez on a fly to right and struck out Billy Butler. Hosmer stole second on Butler’s swinging third strike, but it meant little until Cain connected. Cain fouled off three straight fastballs before putting a 393-foot charge into a splitter that didn’t. When third baseman Miguel Cabrera booted David Lough’s grounder, the Royals had the winning run on base. Detroit manager Jim Leyland responded by calling on Coke to replace Valverde. Coke had Lough picked off before delivering a pitch to Mike Moustakas, but first baseman Prince Fielder dropped the ball. Lough raced into second. But Coke sent the game to extra innings when Moustakas flied to left. That only delayed the celebration. The rally came too late to help Shields, who lowered his ERA to 2.79 by holding the Tigers to two runs in seven innings. The Royals are averaging 2.97 runs per nine innings while Shields is in the game. Only Chris Sale, who toils for the White Sox — the league’s poorest-hitting club — gets less support (2.91) among qualifying American League starters. Shields has been remarkably consistent, too. This was his 12th quality starts in 14 outings. He has also allowed two or fewer earned runs in all but one of his last nine starts but is 1-4 with four no-decisions in that span. The victory capped a restorative 7-2 homestand after a momentum-crushing May. The Royals, 30-33, also pulled back to within 5 ½ games of first-place Detroit in the AL Central Division.