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DETROIT (AP) -- Mike Sweeney figured out how to stop hitting the ball hard for outs: homer.

Sweeney broke out of a slump on his 31st birthday with a grand slam and a three-run home run to lead the Kansas City Royals to a 13-7 win over the Detroit Tigers on Thursday.

Ken Harvey also connected for the Royals, who snapped a three-game losing streak and won for just the 13th time in 44 road games this season. Sweeney's slam in the second and three-run homer in the eighth gave him a career-high seven RBI, matching a club record, and his second multihomer game in 11 days.

Sweeney was just 2-for-20 over the previous five games, with one RBI.

"I've hit four or five balls to the wall the last three games, but they all were outs," Sweeney said. "It was a little frustrating, but (hitting coach) Jeff (Pentland) told me my swing was fine, to just keep swinging that way and good things would happen."

The Royals' 13 runs matched their total for the previous four games.

Detroit's All-Star shortstop Carlos Guillen left the game after the fourth inning due to stiffness in his back. He is listed as day to day.

Kansas City starter Jimmy Gobble (6-7) allowed two home runs to Omar Infante and one to Brandon Inge in 5 2-3 innings, but still improved to 2-0 against the Tigers this season.

"Instead of being aggressive, as I usually am, I was nibbling at the plate and I fell behind a lot of guys," Gobble said. "But a win's a win."

Detroit starter Gary Knotts (5-5) allowed eight runs -- seven earned -- and six hits, walking three and striking out four in 4 1-3 innings. It was his shortest stint as a starter since joining the starting rotation on May 14.

"He's (Knotts) done a very good job in the rotation the last couple months," Detroit manager Alan Trammell said. "Today was not a good start. He fell behind. I always call it playing with fire: The more times you get behind hitters, the more times you go to three-ball counts, you can't dodge enough bullets."

The Royals scored an unearned run in the top of the first, and Infante tied it with the second leadoff homer of his career in the bottom half.

In the second, John Buck walked and advanced to second on a single by David DeJesus. Angel Berroa walked to load the bases, and Sweeney followed with the third grand slam of his career to give Kansas City a 5-1 lead.

The Tigers closed to 5-4 in the third on a solo homer by Inge, and Infante's two-run shot. Nook Logan doubled and scored on Infante's ninth homer.

In the eighth, David DeJesus and Berroa had consecutive one-out singles, then Sweeney hit his 18th homer off Danny Patterson. Harvey added a solo home run with two outs to make it 13-7.

Game notes

The seven RBI matched a club record last matched by Raul Ibanez on July 14, 2002. ... The Tigers activated RHP Patterson off the 15-day disabled list before the game and optioned RHP Craig Dingman to Triple-A Toledo. ... Sweeney's grand slam was his first since June 7, 2003, when he hit one in the first game of a doubleheader at Colorado.