The defeat was Minnesota's second consecutive loss by one run, as the White Sox ended up taking the series after the Twins won the first game on Monday.
"We've been swinging good, but these guys have a pitching staff," Twins manager Ron Gardenhire said. "That's the one thing with the [White Sox]. They have a good pitching staff and you're gonna face some tough pitchers. It doesn't matter who they throw out there."
Diamond, coming off his first career shutout, gave up three runs on eight hits over 7 1/3 innings. He also didn't walk a batter for the second straight outing and struck out three.
But Diamond exited the game in the eighth inning, when Alejandro De Aza hit a liner off his right thigh to score Tyler Flowers from third base. Diamond was at just 93 pitches before coming out due to the injury.
It turned out to be a big play, as it ended up being the game-winning hit for the White Sox, with Diamond's throw to home not in time.
"I think it caught me a little off-guard," said Diamond, who added his leg was fine after the game. "It affected my footing more than anything else. I looked up and saw Flowers halfway to home anyway. So I knew he was going to keep going and I rushed the throw a little bit."
The late one-run lead was enough for the White Sox, with Peavy going eight strong innings. Peavy surrendered two runs (one earned) on five hits. He also struck out eight and walked two.
"His fastball's very sneaky," Twins third baseman Danny Valencia said. "It gets on you. He can throw all three of his pitches for strikes, so that makes it even tougher. He did a really good job today."
Chicago took an early advantage, scoring in the first inning on a sacrifice fly from Adam Dunn after De Aza led off the game with a single, stole second and reached third on a groundout from Kevin Youkilis.
The Twins came right back with a run in the first, as Joe Mauer brought home Ben Revere with an RBI groundout after Revere doubled and reached third on an errant pickoff throw from Peavy.
Minnesota took the lead in the second on Valencia's second homer of the year. The solo shot came on a 1-2 count and was Valencia's first homer since April 23.
But the White Sox tied the score in the fifth, when Flowers beat out a potential double play to allow Alex Rios to score from third.
The Twins had a chance to tie it up in the eighth with runners at the corners and two outs after Youkilis made an error on a grounder hit by Revere. But Peavy got Mauer to fly out to left field to end the scoring threat.
"Joe Mauer is Joe Mauer, and this guy is hitting .330 -- you don't want him up in a situation like that," Peavy said. "Decided to stay hard in and try to get him to hit the ball in the air, and fortunately we were able to do that."
Minnesota had another prime chance in the ninth with Brian Dozier at the plate with runners at second and third and two outs against closer Addison Reed.
But Dozier flied out to center to end the game to give the Twins a 4-2 record on their six-game homestand against the Indians and White Sox, with both losses coming by one run.
"We've been playing well," Mauer said. "It's a good ballclub over there. I think we were in every game. Obviously, we got that first one, but we easily could have won these last two, also. That's what good teams do is battle it out and find a way to win."