The Twins took advantage, leaving town with a 2-1 series win. Meanwhile, the Royals are 11 games under .500 (33-44) for the second time this season, and they've squandered a four-day run of top-line starting pitching.
"We didn't get it done," first baseman Billy Butler said. "I thought we swung the bats well. We just couldn't get the big hit we needed. That's the main game. We had more hits than they did. Obviously, the main column is who scores more runs."
If the offensive results were discouraging, at least the Royals could take some solace in Meche's performance.
Meche, who complained of a dead arm and was questionable to pitch earlier this week, was solid. His velocity reached the mid-90s mph all game, and aside from a few command issues, he held Minnesota mostly in check.
"I was a different guy from my last start to this one," said Meche, who had given up a combined 13 runs in his previous two starts.
Meche said he took two days off between starts and reduced his throwing regimen. Altering his routine paid off.
"I threw the first pitch of the game, and I looked up and I saw 95, and I felt like I didn't really reach back and try to throw it," Meche said. "So I knew velocity-wise, I was fine. It was just a matter of pitching."
Meche allowed three runs -- two earned -- and six hits in six innings. He struck out five and walked five while throwing 121 pitches. It was his second-most pitches of the season behind the 132 he threw against Arizona on June 16, the start before his two-game slump began.
On the other side, Kansas City had few answers for Minnesota starter Glen Perkins.
Perkins worked seven solid innings, allowing just one run despite giving up 10 hits.
The Royals weren't totally stymied. They tallied 12 hits, including a career-high four from Billy Butler, but Perkins kept tossing up zeros.
"They made some nice defensive plays and we didn't get the big hit when we needed it," Royals manager Trey Hillman said. "We scattered too many and didn't bunch enough."
It was the first time the Royals had put up 12 hits and scored fewer than two runs since Aug. 29, 1996, at Detroit.
"That's just the way it's rolling right now," Butler said.
The lack of offense led to a 3-0 deficit, but the Royals finally struck back with a run in the bottom of the sixth.
David DeJesus singled and moved to third on a double from Butler. Jose Guillen picked up the RBI, scoring DeJesus on a single to left.
By that time, Kansas City already had fallen behind 1-0 in the top of the second. Michael Cuddyer did the damage, hitting a first-pitch home run into the left-field bullpen.
The Twins added a run in the third, aided by an error from KC second baseman Alberto Callaspo. With two outs and runners on first and second, Joe Crede hit a grounder that snuck under Callaspo's glove, allowing Joe Mauer to score from second.
Mauer, who awoke from a series-long slump, added an RBI single in the sixth inning. He finished 3-for-3 with two walks and lifted his average to .392.
"I felt like I went in there today knowing Meche had great stuff and tried to keep it simple and go up the middle," Mauer said. "It seemed to work. So I felt a lot better today."
The Kansas City bullpen gave up two runs in the eighth as Minnesota pushed its lead to 5-1.
The Royals had runners on base in each of the first four innings, but Perkins worked out of trouble each time.
Guillen grounded into a double play to end a scoring chance in the first, and Brayan Pena did the same in the second.
Hillman mentioned the missed opportunities after the game. He also talked about the Royals' season-long battle with the injury bug. The team announced before the game that shortstop Mike Aviles will have season-ending Tommy John elbow ligament replacement surgery next week. It's just another in a long list of frustrating circumstances. The Royals aren't healthy, and they aren't scoring runs, either.
Meche was in no mood to concede any excuses.
"You get to a point," Meche said, "where you just have to start winning games."