Baker (5-4) faced one batter over the minimum, struck out seven and allowed two hits, both in the fourth inning. Joe Nathan pitched a perfect ninth for his 23rd save in 25 opportunities.
Gil Meche (7-8) was nearly as good for the Royals, whose four-game winning streak ended. After struggling in the first inning, Meche settled down and allowed two runs through seven innings, striking out five.
It was the third win a row for Minnesota (54-51), which traded second baseman Luis Castillo to the New York Mets for two minor leaguers two hours before gametime. The Twins moved within six games of AL wild-card leading Cleveland, which was idle.
"It's a tough situation for us, because he's a great guy and our leadoff guy and he plays the game hard," outfielder Jason Tyner said. "He's going to be missed, but I think we have the talent here to step up."
The Twins didn't pout for long.
Minnesota's first four batters of the game reached against Meche. Mauer dropped a double inside the left-field line to score Tyner and Jason Bartlett.
Several Twins players cited the fast start in helping the team get over the initial shock of seeing a teammate traded.
"Right now, we know we've got to battle and that's what we're going to do until we're either in it or we're out of it," Bartlett said.
Mauer singled in Tyner in the eighth to make it 3-1. Tyner went 3-for-4 and Mauer finished with two hits.
The back-to-back hits were the only offense the Royals could muster against Baker.
"You have to give him a lot of credit," Royals manager Buddy Bell said. "If we could've got some runs early, it might've been different. But it's not always the negative. I think you have to give (Baker) credit."
Meche avoided further damage in the first by getting Torii Hunter to ground into a double play with runners on first and second and nobody out. Jason Kubel followed by launching a shot into the upper deck in right field that landed foul by only a few feet. Meche struck him out three pitches later.
The 28-year-old then retired 19 of the next 23 batters he faced.
"It's been something weird this year," Meche said. "For some reason every time I give up runs in the first inning, I just shut 'em down and take off the rest of the game."
Baker looked up at the scoreboard before the eighth inning and figured Nathan would be brought in to pitch the ninth.
"I want to know what my last inning is so I can let it fly," Baker said.
Despite the Castillo trade, Twins general manager Terry Ryan told reporters before the game that the team is not giving up on reaching the playoffs this season.
"A tough day," Twins manager Ron Gardenhire said. "But the guys came out and played. And that's all that we can do is come out and play."
Several Royals players are also on the trading block. Octavio Dotel is one of the most sought after players on the market. Grudzielanek and Reggie Sanders also could be dealt before Tuesday's non-waiver trade deadline.
Kansas City starters have allowed just five earned runs in 20 innings (2.25 ERA) this season at the Metrodome. But all it took was a rough start to hand Meche his second straight loss.
"I had Mauer where I want him, a 1-and-2 count," Meche said. "If I hit my location, I wouldn't say it's a bad pitch. But in that situation, you maybe want to throw something else. But that's kind of a second guess after the fact."
- Tyner replaced Castillo in the Twins' leadoff spot and narrowly missed his second career home run in the fifth. Tyner hit his first career homer in 1,220 at-bats Friday against Cleveland.
- Grudzielanek stole his first base of the season in the fourth.
- Three quarters of DeJesus' broken bat in the sixth inning flew into the seats along the first-base line.