"I wasn't commanding my offspeed stuff early, kind of found that later in the game," Giolito said. "Just throwing the ball over the plate, letting them hit it and the defense was spectacular today … just a day for me where everything kind of came together as far as the defense behind me and the offense supporting me."
Five Chicago relievers combined to allow one run in the final three innings, with Joakim Soria recording the final four outs for his fifth save in seven chances.
The White Sox scored four runs in the first while winning for the third time in five games after previously losing six of seven.
Giolito gave Chicago back-to-back strong starts in the doubleheader after Reynaldo Lopez pitched seven scoreless innings in the first game, which was part of the makeup for three postponed games due to snow during the teams' April series in Minnesota.
"These are two of our youngest guys and they continue to evolve in different ways," White Sox manager Rick Renteria said. "Lucas is really grinding right now and trying to find his way back to what he was as he finished the latter part of the season with us last year, and Lopez continues to grow and kind of refine, and is getting after it. Both of them being big pieces for us that continue to navigate a Major League game, which is not easy."
Giolito had allowed 12 runs in 7 1/3 innings over his previous two starts. He entered the game second-to-last in the Majors in ERA (7.53) and third-to-last in walks per nine innings (6.05), but the 23-year-old right-hander was more under control on Tuesday.
Giolito's only two walks came to the first two batters in the third inning, and both came around to score. But Giolito stranded five baserunners combined in the second, third and fourth innings and retired seven of the final eight batters he faced.
"The offense gave me a nice lead real early, so we just kind of took it and ran with it," Giolito said. "Kind of got out of sorts in the third inning, but was able to kind of bring it back and pound the strike zone, mix it up really well."
The Twins had runners on the corners with two outs in the ninth after Soria hit pinch-hitter Brian Dozier and surrendered a single to Robbie Grossman. But Soria got Eddie Rosario to ground out to end the threat.
MOMENTS THAT MATTERED The White Sox jumped on Minnesota starter Zack Littell, who was making his Major League debut. Sanchez doubled with one out in the first inning and Abreu followed with his 10th homer of the season.
Newly recalled catcher Kevan Smith laced an RBI single to right field, scoring Tim Anderson, and Adam Engel finished the four-run inning with an RBI double.
"It's was good for them to bounce back because that's tough, and then you're doing it within 45, 50 minutes of the first one," Renteria said of starting strong in the second game after losing the first on a three-run homer in the eighth inning. "You got to put it to bed as quickly as possible and they did. They came out, they knew we had another game to play and they went out and did what they needed to do."
HE SAID IT "He still continues to evolve. He's still a work in progress." -- Renteria, on Giolito
MITEL REPLAY OF THE DAY Reliever Chris Volstad executed the second pickoff of a baserunner on the day for Chicago by nabbing Ehire Adrianza at second base during the seventh inning.
Adrianza was originally called safe after he was forced to dive back when Volstad spun and threw to second baseman Yoan Moncada. The replay showed Moncada got the tag down before Adrianza's hand reached the base.
UP NEXT Hector Santiago (1-2, 5.10 ERA) will make his return to Target Field for the first time since signing with the White Sox in the offseason in a 7:10 p.m. CT start on Wednesday. The left-hander pitched for Minnesota from 2016-17. Santiago is 1-2 with a 6.59 ERA in six starts this season, including a loss to the Twins in Chicago on May 5 when he gave up eight earned runs in 3 1/3 innings. The Twins will send Jake Odorizzi (3-2, 4.14) to the mound.
Brian Hall is a contributor to MLB.com based in Minnesota.