The Cardinals haven't provided much support for Garcia, though.
Joe Mauer homered for the Twins, too, tying the game in the eighth to answer Jason Heyward's solo shot for the Cardinals in the seventh. Blaine Boyer (2-2) pitched the ninth for the victory, after eight dominant innings by Mike Pelfrey in an old-fashioned duel with Garcia.
The Cardinals were shut out in three of Garcia's first five starts since returning from thoracic outlet surgery last summer to alleviate numbness and tingling in his left arm and hand, but he has been unfazed by the low production behind him.
"Just part of the game. There's sometimes where it's the opposite and you're getting a lot of run support and you're not pitching well," said Garcia, who lowered his ERA to 1.76 by pitching into the seventh and allowing only four hits and two walks while striking out four. "The main thing here is the team and doing the best you can to get 'W's."
Seth Maness bailed Garcia out in the seventh after a walk and a single to start the inning, getting Vargas to ground weakly to shortstop for the double play with the bases loaded. Garcia had a 30-inning streak without a walk end on his batter, but there wasn't much to find fault with.
"It's a shame we couldn't make more out of it," said manager Mike Matheny said, adding: "If I were him I'd be pretty confident right now. Every time he's going out there he's taking us deep into games and not giving up many opportunities, and he seems to be able to be one pitch away almost all the time. It's a rough loss."
Thanks to Vargas, whose drive into the right-field seats off a slow curveball from Carlos Villanueva (3-2) was just his fifth hit in 27 at-bats since being recalled from Triple-A Rochester. St. Louis lost for the first time in 35 games this year when leading after seven.
"When I go out there and I throw the pitch I want and get beat there's not much I can do," Villanueva said. "We needed somebody to get us back in the dugout there. They chose me and I didn't get it done."
St. Louis still has baseball's best record by a comfortable margin, beginning the day with the only winning percentage above .600. The lineup has slumped lately, though, with only 11 runs over the last five games.
"I wouldn't call it a struggle. Sometimes you've got to give the other team's pitchers credit," Heyward said.
Pelfrey bounced back authoritatively from his worst start of the season, when he allowed 11 hits and eight runs over 3 2-3 innings at Texas. He gave up four hits and one walk while striking out three, the home run by Heyward the only blemish.
Pelfrey got Heyward to ground into a double play earlier, matching teammate Kyle Gibson for the major league lead in groundball double plays induced with 16. Pelfrey lowered his ERA to 2.97.
"You only get so many good opportunities, and that was a real good opportunity," Matheny said. "Then they got the home run there when they needed it. It almost takes the wind out of your sails."
Though this was only two games and the two teams played four straight days including the series in St. Louis to start the week, this was the first time this season the Cardinals were swept.
Cardinals RHP Lance Lynn (strained forearm) has been playing catch, but Matheny hasn't reached the point of seeking daily updates, a sign that Lynn still has a ways to go in his recovery since being placed on the DL a little more than a week ago. "I haven't asked that many questions. He's just progressing nicely," Matheny said.