Dunn, who was hitting .190 and had just 27 hits compared to 57 strikeouts entering the day, remained the No. 3 hitter in the White Sox lineup.
Guillen reiterated that spot won't be changing anytime soon, and Dunn helped back that up on Sunday. He reached base in four of his five plate appearances, going 1-for-2 with a single and three walks.
"I've just been trying to almost get out of this stupid funk that I'm in by one swing, swinging as hard as I can," Dunn said. "And that's really not me, I don't swing as hard as I can, I never have. I needed to just relax and get back to the basics of seeing it and hitting it."
"When I bench him, I'm going to bench him for a day off, not because I'm punishing him," Guillen said. "What can I do? This guy is very important in our lineup. We're just waiting for him to hit, and the only way he's going to hit is to play him."
With Dunn playing first base Saturday and Sunday, Paul Konerko has moved to DH, where he went 3-for-8 on the weekend. While Konerko couldn't pinpoint a reason for Dunn's struggles -- whether it's the transition to the American League, lingering effects from his emergency appendectomy earlier this spring or just bad breaks -- he said the team is confident Dunn will get his numbers up soon.
"There's just a lot going on there," Konerko said. "The shame of it is he started out good at the beginning and had the appendix thing. I think he'll catch a streak. A guy like that can make up a lot of ground quickly with the damage he can do when it all lines up right."