"I think a lot of us have been previous closers coming up through the minors or with other organizations," Neshek said. "Just having that mentality plays a lot into it."
Neshek (3-0), the sidewinder from nearby Brooklyn Park, threw 1 1/3 scoreless innings to lead the way and Justin Morneau added two hits and two RBI to help the Twins cut Chicago's lead in the AL wild-card race to one game.
"No offense against our bullpen or anybody's bullpen, but you don't want to get into a battle of bullpens with them," White Sox first baseman Paul Konerko said. "They have a good one. A great one."
The lights-out bullpen, combined with Hunter's regained power stroke, got the Twins off to a good start in an important three-game series.
Hunter hadn't homered in 17 games, a span of 62 at-bats, before hooking Freddy Garcia's second pitch of the sixth inning around the left-field foul pole for a 4-3 lead. Hunter is 15-for-37 (.405) with four homers and seven RBI against Garcia (11-8), who gave up five runs and 10 hits in 6 1/3 innings.
"Fastball," Garcia said of the pitch Hunter hit. "I missed my spot. I tried to go inside and it was down the middle."
Jermaine Dye homered and Konerko had two hits and an RBI for the defending World Series champions, who have lost three of their last four games.
"They were better in every area, so it makes sense they won the game," Konerko said.
Minnesota boosted its lead in the seventh off Neal Cotts. With Nick Punto on second and one out, Michael Cuddyer was intentionally walked and Morneau lofted a fly ball into shallow center.
Rookie Brian Anderson charged in a little too hard on the play, and the ball bounced over his head, allowing Cuddyer to score from first on the single and error. It was Anderson's first error in 111 career games in the outfield.
Minnesota added another run in the eighth off David Riske when Punto singled home Jason Tyner, who had three hits.
"Today was one of the days people had us picked to lose," Hunter said. "Boof went out there and did his thing."
Facing fifth starter Boof Bonser for the first time, it took the White Sox a while to figure him out.
Konerko doubled off the left-field wall in the fourth, and Dye followed with his 33rd homer, tying the career high he set in 2000 in Kansas City. It put the White Sox ahead 2-1.
Doubles by Hunter and Jason Kubel, and Luis Castillo's sacrifice fly gave the Twins a 3-2 lead in the bottom half.
Bonser left with one out in the sixth inning after giving up a double to Thome and a tying single to Konerko. He allowed three runs and six hits in 5 1/3 innings.
"That's we have to do against these guys," Bonser said. "Keep taking games and get ahead of them."
Earlier this week, White Sox manager Ozzie Guillen said it would be his starting pitchers who determined whether the team returned to the postseason this year, not the powerful offense.
Garcia has been among the inconsistent starters for the White Sox. After starting the year 10-4 with a 4.64 ERA, he is 1-4 with a 5.25 ERA in his last nine starts.
"Freddy threw the ball well," Guillen said. "They got a couple of blooper hits. The score doesn't show how good he threw."
- White Sox C A.J. Pierzynski was booed loudly. Pierzynski was one of the building blocks of the Twins' AL Central title-winning teams from 2002-04, before being traded to San Francisco to make room for Joe Mauer.
- Tyner's bunt single in the fourth was the Twins' 142nd infield hit of the season, which leads the majors.
- Chicago 3B Joe Crede went 0-for-4 and is hitless in his last 16 at-bats.