They caught a break from their losing ways on Saturday.
Conor Gillaspie lined a go-ahead single in the sixth inning and the White Sox rallied to beat the Twins 5-4.
"I thought about crying. If that ball had gone over, I would have," White Sox second baseman Gordon Beckham said.
The White Sox have won just three of their 11 games against Minnesota this season and will try to split the four-game series Sunday. Chicago is 13-33 against the AL Central.
"A win is a win. It doesn't matter how you do it," Reed said. "Hopefully, it gets a little spark in us and starts a little winning streak."
Justin Morneau and Arcia homered for the Twins.
David Purcey (1-1) struck out two in an inning for the win. Reed earned his 28th save in 33 chances.
Mike Pelfrey (4-10) allowed five runs, four earned, in five-plus innings. He walked five, struck out two and hasn't won a start since July 6.
"This is by far the worst season of my career," Pelfrey said. "It started off brutal, and I thought I was getting better for two months, but these last three starts have seemed as (bad) as the first two months."
Gillaspie put the White Sox ahead 5-4 in the sixth on an RBI single off reliever Anthony Swarzak.
Garcia went 1 for 4 in his first White Sox start. Chicago acquired him on July 30 from the Detroit Tigers in a three-team trade that sent right-hander Jake Peavy to the Boston Red Sox. Garcia was called up Friday from Triple-A Charlotte after outfielder Alex Rios was traded to the Texas Rangers.
"I was a little tired yesterday, but I feel great today," Garcia said. "Bad day, I got a base hit, but just got to keep playing and see what happens."
The White Sox went ahead 1-0 in the first inning on Paul Konerko's sacrifice fly with the bases loaded.
Danks hit a leadoff home run in the second inning for a 2-0 lead. The homer was his second of the season and first since May 6.
The White Sox added another run in the inning when right fielder Chris Colabello missed a catch on Gillaspie's fly ball for an error, allowing Beckham to score from first base.
Twins manager Ron Gardenhire was unhappy the game started at 3 p.m., leading to shadows that caused trouble for outfielders.
"These 3 o'clock games, for sightlines, are absolutely terrible," Gardenhire said. "The shadows are brutal for both teams. It was a real tough day for both teams once those shadows came in. It's really, really hard to see the ball.
"They really need to fix that part of the game. Play 1 o'clock games or 6 o'clock or 7 o'clock games or get away from the shadows. It was really tough out there, and that was both sides."
Morneau tied the game in the third inning on a three-run homer. He also hit two home runs, including a grand slam, in Game 1 of Friday's doubleheader against the White Sox.
Rienzo allowed a solo home run to Arcia to put the Twins ahead 4-3.
Arcia also hit a home run in each game of Friday's doubleheader and slugged the winning homer in the second game.
Rienzo allowed four runs and seven hits in 5 1/3 innings in his third major league start. He walked five and struck out five.
"We had two games last night, and I tried to be out there for a long time on the mound to help out the bullpen," Rienzo said. "I battle as hard as I can, but unfortunately my control today wasn't that good. But I'm glad the team won."
Rienzo had a visitor waiting for him. His brother surprised him by arriving from Brazil.
"I want to be better because my family is here," he said. "Next time."
Beckham finished with four walks batting leadoff for the second time this season and fifth time in his career.
"I was joking, I don't know if I've had four walks in a week," he said. "It was different. I don't mind it."
LF Dayan Viciedo was scratched from Chicago's lineup because of a sore left thumb. Tekotte replaced Viciedo in left field and batted ninth. .Josh Willingham remained the DH in the Twins lineup Saturday after he was activated from the disabled list on Friday following knee surgery. Gardenhire said there's no issue with Willingham playing the field. "Getting swings right now is more important and running the bases," Gardenhire said. "He's already played the outfield down (in the minors), so I'm not worried about that."