While Slowey's pitch count reached 26, the game remained scoreless.
"I feel like if there's going to be a time when you're going to have a long inning, the first is probably the one to have it in," Slowey said. "The fact that we kind of came out of it unscathed makes you look back and say, 'Well, maybe I'm not as gassed as I thought I would be.'"
With Slowey on the hill, Boston was able to manufacture a run in the third to take a 1-0 lead. Jacoby Ellsbury extended his hitting streak to 22 games with a single, and he advanced to second on a single by Dustin Pedroia. After a walk to J.D. Drew loaded the bases, Youkilis drove in Ellsbury with a sacrifice fly to center.
"This is a very good baseball team over there with a lineup just full of guys who can hurt you and have quality at-bats," Twins manager Ron Gardenhire said. "Nothing comes easy with them. Slowey really had to work through it tonight and made a lot of good pitches."
It was another long inning for Slowey, but his teammates made it even longer for Red Sox starter Daisuke Matsuzaka in the bottom half of the first.
Span led off the third with his second of four hits, then stole second base and took third on a throwing error by catcher George Kottaras. Joe Mauer collected his 32nd RBI in the month of May when he sacrificed in Span to tie the game at 1.
The Twins then sent up Justin Morneau, who laced a double off the baggie in right. Designated hitter Jason Kubel made it back-to-back doubles, driving in Morneau and giving Minnesota a 2-1 lead.
Kubel would later score on a single by Brendan Harris, who had two hits on the night.
"We swung the bats really well," Slowey said.
That would be all the run support Slowey (7-1) needed, as he allowed just one more run en route to collecting his sixth quality start of the year. Boston's Jason Bay took Slowey deep to left-center to cut Minnesota's lead to 3-2.
The Twins added their fourth and final run in the sixth. Red Sox reliever Manny Delcarmen loaded the bases before Justin Masterson came out of the 'pen. Masterson then hit Michael Cuddyer with a pitch, bringing home Span.
Span, who was held out earlier in the week after experiencing dizziness, tied a career high with his four hits. He scored the first run for Minnesota in the third inning and the final run in the sixth, while also recording a stolen base, his 11th of the season.
"I'm going to be honest, my legs are killing me right now," Span said. "I was on base five times today and running all over the place. But it's fun that way. I'd rather have it that way than being on the bench making right turns instead of left turns."
Three Boston pitchers combined to throw a record-tying six wild pitches on the night, including four by Matsuzaka (0-3). Minnesota only scored once as a result of the wild pitches, but Matsuzaka's pace of play slowed the game considerably.
"I just kept looking at the clock, and I'm like, 'It's 9 o'clock in the sixth inning," Span said. "It seemed like it was taking forever. Maybe that's part of his strategy, but it didn't work tonight."
"We know how he works," Gardenhire said. "He's deliberate. There's nothing wrong with that. That's just the way he pitches. ... But we battled him pretty doggone good, made him throw a lot of pitches."
The Twins' bullpen picked up the game in the seventh and kept the Red Sox off the board. Jose Mijares pitched an inning and a third, Matt Guerrier threw two pitches and induced a double-play grounder, and Joe Nathan tossed a perfect ninth to record his eighth save of the year.
With the win, Minnesota improved to 5-1 on the recent homestand and 19-10 at the Dome this year.
"I think it's very important, especially with the road trip we had, to come in and to win at home," Slowey said. "This is where we're comfortable."