MINNEAPOLIS -- After a pair of pitching duels, Atlanta's offense broke loose and powered the Braves to another series victory.
"He's been just an unbelievable pickup," Braves manager Bobby Cox said. "He just keeps swinging."
The Braves scored four runs in the first inning and built on the lead to support Kris Medlen. Atlanta took two of three in an interleague series between division leaders, a rematch of the thrilling 1991 World Series won by Minnesota in seven games.
After struggling early in the season, the Braves have won or tied their last 12 series since dropping two of three games to Washington from May 4-6. Atlanta is 14-6 over the last 20 games, all played without an off day.
"It was a tough stretch, but it's our job to win ballgames," Glaus said. "Nobody's going to feel sorry for us."
Making his 11th major league start, Medlen (4-1) tossed a career-high eight innings and held the Twins scoreless until Delmon Young's three-run homer with two outs in the seventh.
The Twins didn't get a hit off Medlen until Jason Kubel lined a double with one out in the fifth. The right-hander allowed four hits and struck out five.
"They threw a guy out there today that did everything right," Twins shortstop Trevor Plouffe said.
Tim Hudson lost the series opener 2-1 and Derek Lowe started the next day, a 3-2 win for the Braves. The early offense Sunday helped Medlen settle in and attack a Twins lineup missing its two starting middle infielders.
"Lowe and Hudson were calling me a run hog today," Medlen said. "Any time you get the offense swinging like they did early, it gives you the confidence to go out there and just start throwing strikes."
Glaus, who had three RBIs, hit his 12th and 13th home runs in consecutive at-bats in the fifth and seventh. It was the 29th multihomer game of his career and first since Aug. 9, 2008.
The slugger played only 14 games for St. Louis last season because of shoulder surgery and did not hit a home run. He signed a one-year, $1.75 million contract with the Braves during the offseason.
Glaus hit just .194 in April, but got rolling in May. Since May 1, he leads the NL with 40 RBIs. His batting average has improved to .290.
Martin Prado homered in the second and had three hits, raising his season total to an NL-best 90.
Twins manager Ron Gardenhire gave center fielder and leadoff hitter Denard Span his first day off this season. Michael Cuddyer got his first start at center in Target Field and Nick Punto hit leadoff.
Twins starter Kevin Slowey (7-4) entered with a three-game win streak and a 0.64 ERA in June. After allowing six runs (five earned) on nine hits in 4 2/3 innings, the right-hander's win streak is over and his June ERA stands at 2.89.
Despite a solid 3.84 ERA, Slowey has failed to pitch past the fifth inning in nine of his 13 starts.
"It's disappointing to go out there and feel like you put your team behind the 8-ball right away," Slowey said. "Even in that inning I felt like I made some good pitches."
Atlanta took the final two games from the Twins despite playing without third baseman Chipper Jones. He was a late scratch from Saturday's game and sat out Sunday with an injured right ring finger. He is day to day.
Jason Heyward started the Braves' four-run first with a broken-bat RBI double down the right-field line.
"Any time you break a guy's bat, you don't expect it to go that far," Slowey said.
Sunday's win was the perfect way to end a season-long 11-game road trip for Atlanta. Since May 18, the Braves are 19-7.
Several players have stepped up during the recent run. Brooks Conrad filled in at third base for Jones on Saturday and delivered the winning suicide squeeze bunt in the ninth. Medlen continues to pitch well in the absence of Jair Jurrjens, and Glaus is on a roll.
"That's what good teams do," Hinske said. "Everyone gets prepared to step up when needed and win ballgames. You're seeing that happen with us because everyone understands what needs to be done to compete."
Young's home run extended his hitting streak to 10 games. He has 13 RBIs during the streak and is second on the Twins with 43.
Twins 2B Orlando Hudson took batting practice and hopes to return from a sprained left wrist on Tuesday. ... Braves infielder Omar Infante remains out after fouling a ball off the top of his right foot Friday. Infante will likely miss the next two or three games. ... Twins RHP Clay Condrey, who has yet to pitch this season because of an elbow injury, went to Florida to get some work in extended spring training. ... Twins pitching coach Rick Anderson missed the game to attend his daughter's high school graduation.