Quintana (8-6) won for the first time since he last faced the Twins, on Aug. 16. He allowed one run while scattering eight hits, striking out five and walking two.
The drought had nothing to do with Quintana's pitching.
During his winless streak, Quintana was 0-2 in five starts. He had a 3.03 ERA over that stretch, while being backed by a total of five runs -- two in the past four games.
Quintana and the White Sox led 4-1 in the seventh, but the Twins scored two in in the seventh to give the left-hander and the White Sox a scare.
"When he leaves and all of a sudden they start somewhat of a rally, you don't want to go down that road," White Sox manager Robin Ventura said. "But we've seen it enough this year that a lot of his starts seem to go for naught. But tonight they at least came back and the bullpen did a nice job."
Quintana leads the majors with an American League-record 17 no-decisions.
"He's done a very good job. He's been very mature about it, of going through it that he's not pointing any fingers or showing any emotion when he's walking through the clubhouse," Ventura said. "He's the same every day. He just wants to win. And he wants us to win first and hopefully he gets the win, but he really hasn't shown a lot of emotions other than if we lose or not. Him pitching, he's getting better all the time. You'd just like to see him get those wins."
After a 2-15 stretch, the White Sox won the first two games of the series against the Twins for their first series victory since Aug. 27-29 against Houston. They have won five straight against the Twins.
White Sox closer Addison Reed pitched a scoreless ninth for his 38th save in 44 opportunities, benefiting from Alejandro De Aza's leaping catch of Trevor Plouffe's flyball against the wall in center field for the second out.
Brian Dozier had three hits and scored two runs for the Twins, who have lost six of seven. Minnesota starter Mike Pelfrey (5-13) went 4 1-3 innings, allowing three runs and nine hits. He has lost three straight starts for the first time since July 5-19, 2010, with the New York Mets.
It was the second straight start he got an early hook. In his last start, he was pulled in the fourth inning, after allowing seven earned runs in an 18-3 loss to Oakland.
"I thought April was bad, but if you look at the numbers, this is probably worse," Pelfrey said. "It's definitely not how I envisioned finishing the year. Hopefully I can try and finish on a positive note. I think the biggest thing was I was commanding my second and third pitch."
Pelfrey is 0-3 with a 6.04 ERA in his last five starts. The White Sox are hitting.345 (38 for 110) this season.
"It's all about strikes, attacking these hitters and not getting in the 3-2 counts. That's where it ended up an awful lot, just trying to be too fine. You need to get quick outs," Twins manager Ron Gardenhire said. "As the game was going along, you guys saw it, we all felt it, it went nowhere. 96 pitches in 4 1-3 innings, that's just too many pitches."
Marcus Semien put the White Sox ahead in the second inning with an RBI single.
After White Sox second baseman Gordon Beckham was unable to turn a double play, Dozier stole second and scored on Plouffe's double in the third inning. The White Sox got the lead back in the fifth when De Aza led off with a single and scored from first on Alexei Ramirez's double. Viciedo followed with an RBI single to give Chicago a 3-1 lead.
Viciedo's RBI single in the sixth extended the lead to 4-1.
In the seventh inning with runners on first and third and no outs, Plouffe hit a ball off reliever Jacob Petricka's left wrist to score a run. Oswaldo Arcia followed with a grounder to shortstop Ramirez, who flipped for the force out, but Beckham tried to turn a double play and made a wild throw to first allowing a run to score to cut the White Sox lead to 4-3.
Ventura said that LHP Hector Santiago would be skipped in the rotation. RHP Andre Rienzo will go on normal rest on Friday after Thursday's day off. ... Gardenhire wouldn't commit to giving RHP Liam Hendricks his next start after he gave up seven runs in 2-3 of an inning on Monday night. RHP Cole DeVries, who gave up four runs in five innings of relief on Monday, is an option to take Hendricks' spot in the rotation. ... Twins GM Terry Ryan gave an update on C Joe Mauer (concussion), who didn't travel with the team on their trip. Ryan said Mauer is symptom free and may rejoin the team in the next couple days. ... The White Sox committed three errors.