Royals manager Trey Hillman, left, argues with umpire Fieldin Culbreth after Mike Aviles was called out in the sixth inning. Hillman argued that the ball should have been ruled foul since it was tipped off of Aviles' foot. Hillman lost the argument, and the Royals lost their 11th straight, 5-1, Thursday in Kansas City, Mo.

Kansas City, Mo. ? If Jose Guillen’s profanity-filled tirade was meant to light a fire under the lethargic Kansas City Royals, Kevin Slowey did a good job of dousing the flames.

The Minnesota right-hander threw his first major-league complete game, and Carlos Gomez had four hits and two RBIs, leading the Twins to a 5-1 victory Thursday night that stretched KC’s losing streak to 11 straight.

It’s the longest skid in the majors this year and Kansas City’s worst since a 13-game skid May 12-25, 2006. The Royals’ 21-33 record is the worst in the American League except for Seattle’s 20-34.

“It’s no fun going out there and losing every day,” said David DeJesus, who ruined Slowey’s shutout when he doubled in the ninth and scored on Alex Gordon’s double. “I didn’t think this was going to happen. We have too good of players on our team right now. But it’s happening.”

Guillen went on his tirade after Wednesday night’s loss, calling the Royals “babies” who didn’t know how to win. He had one of the Royals’ four singles off Slowey (2-4), who did not allow a runner as far as second base until DeJesus and Gordon doubled. The right-hander struck out six and walked none.

Until Gordon’s RBI double in the ninth, he had pitched 14 straight scoreless innings for the Twins, who completed a 5-1 trip to Detroit and Kansas City.

“Obviously, this is a big win for the team,” said Slowey, who has won two straight after losing his first four decisions. “With some good pitches and some great defensive help, you can go a long way. I’m a lot more comfortable now, but I think it will be awhile before I’m nonchalant about it.”

The poster boy for the Royals’ futility streak could be Luke Hochevar, who has started three of the 11 games and has seen his team score only one run for him. The rookie right-hander started the first game of the streak when Boston’s Jon Lester no-hit KC in a 7-0 victory. Next he lost 6-0 to Jesse Litsch’s complete-game seven-hitter in Toronto.

Against the Twins, Hochevar (3-5) went 5 1/3 innings, giving up nine hits and five runs, with three walks and three strikeouts.

“I just fell behind the counts, got in the hitters’ counts,” he said. “I had to throw my best pitch. Ultimately, they’re sitting on it. They were able to get pitches over the plate and put the ball in play.”

Michael Cuddyer’s RBI single scored Joe Mauer with Minnesota’s first run in the fourth, then the Twins loaded the bases with two out. But DeJesus, playing left field, made a terrific running catch of Mike Lamb’s foul pop for the third out.

Gomez, the Twins’ leadoff hitter, doubled in the fifth and made it 2-0 on Mauer’s double.

After Jason Kubel and Craig Monroe singled leading off the sixth, Lamb laid down what looked like a sacrifice bunt. But after Hochevar fielded the ball, he paused too long looking at third and failed to get the ball to first in time to retire Lamb. So the bunt went as a base hit and the bases were loaded with no out.

After Brendan Harris’ sacrifice fly made it 3-0, Hochevar was relieved by Ron Mahay, who gave up a two-run single to Gomez.

It was the second consecutive strong start by Slowey, who stopped a personal five-game losing streak in his previous start at Detroit.

“There’s still room (for improvement) believe it or not. There’s still room,” Slowey said. “We made some phenomenal defensive plays, a couple of double plays.”

Slowey kept the Royals at bay by consistently going 0-1 and 1-2 on hitters.

“The guy just filled up the strike zone,” said Royals manager Trey Hillman. “We squared some pitches up that we didn’t necessarily smoke and we didn’t necessarily drive. We could have done a better job, no doubt. Thankfully, it wasn’t a shutout.

“It’s a heck of a process, basically, when you’re trying to teach it at this level against this level. It’s not easy.”

Notes: Eight times in the past 10 years Kansas City has endured losing streaks of nine or more games. … Slowey was making just his 17th major league start. … Looking for some offensive punch, the Royals sent struggling DH/first baseman Billy Butler to Triple-A Omaha and called up infielder Mike Aviles, a 27-year-old non-roster invitee. Aviles was 0-for-3 and struck out. … The Twins claimed LHP Craig Breslow off waivers from Cleveland and transferred RHP Pat Neshek from the 15- to the 60-day DL.