"I don't usually do too much out there after a game, but with everything that's been going on and not doing well yesterday I was excited today to get that one," said Perkins, who notched his 19th save in 22 tries after giving up two runs to blow one the night before.
Adam Eaton led off with a triple and scored on Gordon Beckham's sacrifice fly. Pinch-hitter Paul Konerko then smacked a single up the middle, but Perkins struck out sluggers Jose Abreu and Dunn to delight the standing crowd of 32,647.
"It's never a comfortable at-bat, because if he hits it he's going to hit it far," Perkins said. "So it was just stay with fastballs ... and make him beat me."
Dunn is 0 for 11 with eight strikeouts in his career against Perkins.
With the Twins trailing 2-1, Mauer's drive in the fifth inning soared over left fielder Alejandro De Aza and landed about halfway up the wall. Kendrys Morales hit the next pitch for an RBI single against Andre Rienzo (4-5), who lost his fifth straight start.
"You have to be a really good outfielder to be able to make that play," White Sox manager Robin Ventura said of De Aza. "I see him making a good effort at that. It just started cutting away from him."
Correia (4-8) gave up five runs or more in five of his first 12 starts, sliding toward replacement in the rotation, but he has pitched well in three turns since. In 18 innings, Correia has allowed a total of two earned runs. He gave up five hits and two walks on this picture-perfect first-day-of-summer afternoon.
The Twins, who took a five-game losing streak into this series, have a 2.41 ERA for their starters over the last 11 games.
"I've made some slight adjustments and I've been steadily getting a little better, but I think the ball's just kind of bouncing my way a little more than it had," Correia said.
Center fielder Sam Fuld tried to dive for a two-out sinking liner by Conor Gillaspie in the first inning, but the ball skipped in front of and past him for a triple and Abreu followed with an RBI single. Then third baseman Eduardo Escobar bungled a routine ground ball by letting it slide between his legs to start the second inning, his first of two errors, and Beckham was hit by a bases-loaded pitch to force in an unearned run.
The Brazilian-born Rienzo, who debuted for the White Sox last summer, could be in trouble with his spot. After going 4-0 in his first six starts in replacing the injured Felipe Paulino, Rienzo has an 8.87 ERA.
Rienzo gave up seven hits and two walks in 4 1/3 innings.
The Twins hit three straight two-out singles in the second inning to load the bases, and Fuld walked to force in the first run. Then Rienzo hit Brian Dozier with a pitch to put two runners on for Mauer in the fifth inning, setting the struggling six-time All-Star and three-time batting champion up for just his fourth multi-RBI game this season. Two of those have been in this series.
"It's a good time for Mauer and a bad time for me," Rienzo said.
Mauer has 18 of his 20 RBIs this season at Target Field.
"It gets frustrating when they don't fall, but it's nice to come through in those situations for your team," he said.
Gillaspie went 2 for 4 to raise his average to .340, but he doesn't have enough at-bats to qualify yet for the league batting lead. ... Twins RF Oswaldo Arcia is hitless in his last 27 at-bats. ... The White Sox will send John Danks (6-5, 3.97) to the mound for the series finale Sunday, and Phil Hughes (7-3, 3.09 ERA) will pitch for the Twins. Danks has a 5.70 ERA in six road starts this season. Hughes gave up three HRs in his last home start, the only time a team has taken him deep in his last eight turns.