Updated

Lorenzo Cain's RBI single capped a three- run third inning and proved to be the difference in the Kansas City Royals' 3-2 victory over the Detroit Tigers Monday in the opener of a three-game set at Kauffman Stadium.

The Royals did all their damage in the decisive third frame, with Salvador Perez plating a pair of runs with a triple before scoring on Cain's base hit to provide just enough run support for starter Jeremy Guthrie.

Guthrie (7-3) limited the potent Tigers lineup to two runs on six hits and three walks over 6 1/3 frames to help the Royals notch their sixth straight victory, the club's longest win streak since taking seven in a row from Sept. 10-17, 2011.

Three Kansas City relievers combined for 1 2/3 scoreless innings before Greg Holland hurled a perfect ninth to nail down his 13th save.

Miguel Cabrera clubbed a two-run homer to account for Detroit's offense, while starter Doug Fister (5-4) went the distance in defeat, giving up three runs on nine hits over eight innings.

"I felt like I made some timely pitches when I needed to, but they hit a couple balls that found holes," Fister said. "That's what they needed to do."

Cabrera got the Tigers on the board in the top of the third when he followed Torii Hunter's one-out double with a towering fly ball over the left-field wall to make it 2-0.

The Royals quickly responded in the bottom half, as Alcides Escobar smacked a leadoff single and moved to third on Eric Hosmer's one-out base hit to right.

Perez then ripped a triple to the gap in right-center field that landed just out of the reach of a diving Avisail Garcia, allowing Escobar and Hosmer to score and tie the game at 2-2.

After Billy Butler grounded out, Cain legged out an infield single to plate Perez for a 3-2 lead.

"With a runner on third and the game tied, 2-2, I'm thinking as soon as I hit it about getting down the line as fast as possible," Cain remarked. "I was able to get a hit out of it."

Guthrie kept the Tigers out of scoring position over the next three frames before running into trouble in the seventh, when he served up a one-out single to Garcia before plunking Andy Dirks.

Aaron Crow entered from the bullpen and quickly quelled the threat by flying out Hunter and striking out Cabrera to end the inning.

Tim Collins and Kelvin Herrera combined to keep the Tigers off the board in the eighth before Holland retired the visitors in order in the ninth.

Game Notes

Guthrie has pitched at least six innings in 12 of his 13 starts this season ... It was Fister's sixth career complete game ... Prior to the game the Royals announced the team has signed infielder Hunter Dozier, the eighth overall pick in last week's First-Year Player Draft ... Detroit went 1-for-5 with runners in scoring position and left eight men on base.