Dunn hit a two-run shot deep into the right-field seats off Jose Valverde in the ninth Saturday and Chicago went on to beat the Tigers 3-2.
Detroit defeated the White Sox 5-4 on Friday night when Jhonny Peralta hit a two-run shot with one out in the ninth. There was also one out when Dunn hit his 422-foot drive off Valverde (2-1).
"We needed to win this game today," Dunn said. "I definitely didn't want to chase anything -- just got a pitch that I could get in the air and it happened to go out."
Detroit's Delmon Young went hitless in his first game back from a seven-day suspension following his April 27 arrest in New York.
It was Valverde's second blown save of the season. He was perfect in 49 chances in 2011.
"Last year is over," Valverde said. "The closer, everybody knows, it's not easy. One pitch can be the game, like it was today. Adam Dunn got it."
Dunn endured a horrendous 2011 season, his first with the White Sox. After hitting at least 38 homers for seven straight years, he managed only 11 last season to go along with a .159 batting average.
He's back to his productive self so far in 2012, hitting .250 with eight homers.
"It's good," Dunn said. "This is kind of what I expect to do."
Paul Konerko also went deep for Chicago.
The Tigers scratched out their two runs in the second on RBI singles by Andy Dirks and Jackson.
The White Sox trailed 2-0 before Konerko's solo shot in the seventh. Alejandro De Aza started the ninth with a single and a stolen base. He was sacrificed to third and Dunn -- always a strikeout risk -- made solid contact to put Chicago ahead.
Jones had pitched the bottom of the eighth, and Hector Santiago came on to try to close it out, but a walk and a double put Chicago's slim lead in jeopardy. Reed, who hasn't allowed a run this season, got the best of Jackson to preserve the win.
Gavin Floyd allowed two runs and seven hits in seven innings for the White Sox.
Jackson's run-scoring hit actually deflected off Morel and past Ramirez, who looked as though he might have been in position to keep the ball at least in the infield and prevent the runner on second from scoring.
"You just kind of stay positive and continue to try to make pitches," Floyd said. "Got the ball on the ground, and it seemed like they were just missing guys."
Floyd retired 12 in a row starting in the third. In his last three starts, he's allowed four runs in 21 innings.
Detroit's Max Scherzer yielded a run and four hits in seven innings. He struck out nine without a walk. Showing none of the control trouble that plagued him in a seven-walk performance last weekend against the Yankees, Scherzer retired the first 11 White Sox before Dunn lined a single to right.
Chicago's second hit nearly ended Scherzer's outing. In the fifth, A.J. Pierzynski's line drive up the middle hit Scherzer's right foot during the pitcher's follow through. The right-hander picked up the ball and threw wildly to first, and the play went for an infield single and an error, with Pierzynski ending up on second.
Scherzer stayed in the game and got out of the inning on a flyout and two strikeouts. He allowed a single to De Aza in the sixth -- then promptly picked him off first. Konerko broke up the shutout an inning later with a homer to left.
Young was reinstated from the restricted list Friday after his suspension, but he didn't play that night. He received mostly cheers and a few scattered boos from the home crowd for his first plate appearance.