That alteration produced only three hits, and the lack of offense caught up with the Sox in a 2-0 loss to the Los Angeles Angels.
"I think I'm going to move a couple guys down," Guillen said after the game. "Right now, I don't know who."
But the Sox weren't so fortunate in the eighth when the Angels broke through on Torii Hunter's single off Dotel, Garret Anderson's single on a 3-0 pitch off Matt Thornton that grazed off the glove of a diving Dye in right and Mike Napoli's sacrifice fly.
The Angels added an insurance run in the inning on Robb Quinlan's two-out hit off Scott Linebrink.
"I'm pleased with the way I threw, but ultimately, we're here to win games," Danks said.
The Sox never got any of their four baserunners past first base until Carlos Quentin hit a double with one out in the ninth. Guillen employed his 24th lineup of the season in an effort to find the right combination for a team that lacks speed and ranked 13th in the American League with a .243 batting average.
The changes, however, didn't involve Jim Thome, who went 0-for-3 and is 2-for-12 on this trip. His batting average dipped to .209.
Before the game, Guillen said the Sox's seven-run production Monday prevented him from making more changes. He promoted Dye, who was coming off a four-hit game and was hitting .324 during his first 10 games of May.
He also wanted to take some pressure off Konerko, who is 0-for-8 in this series and 4-for-20 on the trip.
Dye and Konerko were a combined 0-for-7 Tuesday.
Konerko hasn't hit a home run since April 27, one day before feeling severe discomfort after getting jammed by Baltimore's Daniel Cabrera in damp 38-degree conditions.
This marked the first time this season that Dye batted fourth and Konerko fifth with Thome in the lineup. Konerko batted .292 in 48 at-bats in the fifth spot last year and didn't seem to mind the change.
"I don't think its a big deal to me," Konerko said before the game. "I still get four at-bats. I don't mind it. Those (lineup changes) don't mean a big deal to me. That's the way I've always went at it."
Dye echoed Konerko's feelings.
"I don't think it matters where any of the three of us hit," Dye said.
"If a guy is swinging the bat better, they are going to put guys in different spots and see if they can get this lineup going."