Runelvys Hernandez -- who was making his first start of the season -- and relievers Elmer Dessens and Ambiorix Burgos held the Twins to four hits.
Baker, who gave up six hits and four runs (two unearned) in his previous start against the Angels, held the Royals to three runs and seven hits -- three of them by Mark Grudzielanek -- in seven innings. He struck out six and walked none, throwing 66 strikes in 95 pitches.
"Three runs in seven innings, that's pretty good pitching, really," Gardenhire said. "He pitched his tail off. Hernandez just pitched better. We didn't swing the bats well tonight. We hit a few balls hard. He definitely shut us down. It was a disappointing night for us."
Grudzielanek led off the fourth with a triple and scored on Reggie Sanders' groundout.
Baker yielded two runs with two out in the sixth to break a 1-1 tie. Grudzielanek singled and scored on Matt Stairs' double off the center-field fence. It was Stairs' first hit of the season in his ninth at-bat. He scored on Emil Brown's single.
"It wasn't a good pitch. I wouldn't necessarily say it was a bad pitch," Baker said of the pitch Stairs hit. "It was probably the right pitch, but the wrong location. I made some good pitches previously that, probably a majority of the time, would have got me out of the inning and then it would have been a different ballgame. I gave up a bloop hit and then a big hit."
Hernandez, whom the Royals optioned to Triple-A Omaha to start the season after he reported to Spring Training overweight and out of shape, gave up a leadoff single to Shannon Stewart, but stranded him at third base.
Hernandez, who was 1-2 with a 10.67 ERA in three starts with Omaha, retired 13 in a row after Stewart's hit before Justin Morneau homered to right-center with one out in the fifth.
Morneau snapped an 0-for-19 skid with his fifth home run, which ties Torii Hunter for the team lead. Morneau's home run was his first since he homered in back-to-back games on April 11-12 against the Athletics.
Hernandez left after seven innings, giving up just two hits, walking none and striking out one.
"[Hernandez] used his breaking ball, had a good changeup and located his fastball," Gardenhire said. "He pretty much had his way with the strike zone. He used all of his pitches more than anything else. His changeup to left-handers was pretty good. He did what he had to do. He worked ahead, kept people off balance and put you in a defensive position all the time when you're at the plate. That's where we were at all night. He was getting ahead and forcing the issue. When a guy is on, he's on -- and he was on tonight."
Said Rondell White, who went 0-for-4: "He got the job done. When we didn't score early, he pitched with confidence. He had a good fastball, 91-93 [mph] and a good slider.
"It's not that we're swinging the bats bad. We're just not lucky right now. That's the way baseball is. You've got to come out. You have to. Torii could have had two hits. Shannon could have had three hits. It didn't work out."
Lew Ford singled in the eighth off Dessens to extend his hitting streak to five games. Joe Mauer singled with two out in the ninth off Burgos for the final Twins hit.
The game lasted just 2:07 as both starters worked fast and there were no walks in the game.
"That's what I like to do, keep a good pace, get your team in the dugout quickly as possible," Baker said.
Now the Twins just need the pitching and offense to show up in the same game.
"It's going to happen," Baker said. "It's just part of baseball, part of life. We'll get everything clicking and on the same page, no doubt in my mind."