Valverde took his first loss of the year and first blown save since Opening Day against the Red Sox.
"Everybody knows Adam Dunn is a good hitter," said Valverde, whose ERA jumped from 5.06 to 6.17 with the two earned runs. "I missed a little bit and he got it. There's nothing I can do, you know what I mean? I did my job yesterday. I didn't do it today. And now I got to get ready for tomorrow."
Alejandro De Aza led off the ninth with a single back up the middle and advanced to third on a stolen base and sacrifice bunt. Dunn got a 1-0 fastball down the heart of the plate and took it deep.
Valverde pitched a scoreless ninth inning Friday night and got credit for the win when Jhonny Peralta belted a walk-off home run. But prior to that outing, the 34-year-old closer had pitched only once in the previous 12 days. Manager Jim Leyland thought rust might be an issue.
"He's struggling a little bit, obviously, right now," Leyland said. "Maybe I got to get him out there a little bit more. He threw the ball down right into the groove of the swing and Dunn hit it. He's just struggling a bit right now and that can happen to closers from time to time."
The home run erased the work of Max Scherzer, who bounced back from allowing a career-high seven walks to the Yankees in his last start. Scherzer had full command of his pitches facing the White Sox (13-14), allowing only four hits and one run while striking out nine and not walking anyone in seven innings.
The 27-year-old said he looked at video with Leyland and pitching coach Jeff Jones from last season, when he started 6-0 with a 3.20 ERA, and came to the conclusion he needed to correct a mechanical issue with his hands.
"We made the mechanical change of breaking my hands higher and we did countless reps of trying to make that feel natural," Scherzer said. "The bullpen work, getting on the mound and just constantly thinking about having my hands break higher."
The work paid off as Scherzer stayed ahead in the count throughout the entire game. Only four times did he face three-ball counts. Three of those came in the third inning and resulted in two strikeouts and a harmless tapper in front of home plate. The fourth came in the seventh, and he forced a soft flyout to third base.
"He is so good," Dunn said. "Especially when he's pounding the strike zone like he did tonight. He's good when he's throwing strikes. He definitely shut it down."
The only damage the White Sox could do to Scherzer came in the seventh on a solo shot from Paul Konerko. Konerko drove the first pitch he saw over the left-field wall to make the score 2-1.
The Tigers (13-13) scored both of their runs early off White Sox starter Gavin Floyd. Floyd took a no-hitter into the seventh inning in his previous start, but found himself in trouble early.
Floyd allowed two runs on four singles in the second inning, which resulted in two runs. Andy Dirks hit a well-placed RBI single in the gap between shortstop and third. And two batters later, Austin Jackson attacked the same area for an RBI single of his own.
After escaping the second, Floyd retired 15 of the final 18 batters he faced. And only one batter, Dirks, made it to scoring position.
"Good pitchers are always going to put down some good hitting," catcher Alex Avila said. "And that's baseball. There's going to be stretches you're not going to hit, then you're going to hit. There's going to be games where you're going to score a ton of runs, then you're not. That's part of the game until you can find some form of consistency."
Sitting with a .500 record, it's clear the Tigers haven't found it yet.