The loss spoiled a two-home run game by first baseman Paul Konerko, Nos. 15 and 16 on the season, the latter giving him a share of the Major League lead.
The first inning was the biggest struggle for Floyd, as he threw 33 pitches and allowed five consecutive batters to reach base. The Rangers piled on three runs before the White Sox batted.
"It's kind of tough to understand everything," Floyd said. "I think that was one of those where you just try to learn from it. I had two good outings before, hopefully I can put this behind me."
Floyd had not given up more than three runs in his previous two starts, but that streak was broken two batters into the second inning when Michael Young plated Elvis Andrus to bring the score to 4-2.
In all, the Rangers tallied six runs on eight hits against Floyd, who earned the loss (2-6). He is now 1-2, with a 7.38 ERA lifetime against Texas. Floyd's 2 2/3 innings mark his shortest career start at U.S. Cellular Field.
"Maybe the first year in his career here, but I don't think I've ever seen him this bad," said White Sox manager Ozzie Guillen. "Bouncing balls, getting hit hard. That's the first time I've seen him pitching this way. This kid, every time he is in there, we believe we have a chance. Nothing was working with him.
"I tried to stay with [Floyd] as long as I can, because our bullpen is very thin, and I couldn't," added Guillen, who said prior to the game that he wanted to rest his tired relief corps.
The White Sox answered the Rangers' first-inning surge with two runs of their own, as Juan Pierre smacked a single and stole second base. He scored on Omar Vizquel's double down the right field-line. Vizquel, in turn, was driven in on Konerko's RBI groundout.
But the White Sox offense went dormant for the remainder of the game, except for Konerko, who slugged a solo home run in the sixth and a two-run shot in the eighth.
"We had a couple of games early in the year where our pitching was there and we weren't scoring a whole bunch of runs," Konerko said. "I think lately it's been the reverse of that. It's frustrating. It's not fun to lose more than half the time. But there's a ton of games left, and we have to try to keep putting it together. There have been flashes of all facets at some point, and you just have to hope at some point it's going to click."
The White Sox bullpen allowed three runs in the game. Tony Pena continued to do yeoman's work, giving up two runs on a hit in 2 1/3 innings in mop-up work. Randy Williams also pitched two innings of relief. Bobby Jenks pitched the ninth in his first action since tweaking his hamstring in Tampa a week ago. He struck out Matt Treanor, while giving up an infield single to Julio Borbon.
Treanor led the Rangers attack with four RBIs off a home run and an RBI first-inning double.
Scott Feldman (3-5) picked up the win for the Rangers, giving up five runs over the course of eight innings. Of the eight hits the White Sox compiled against Feldman, five were extra-base hits, but all too often, the team could not get the key hit.
"With the exception of Paul Konerko, I threw the ball pretty good," Feldman said. "I hope he gets food poisoning the next time we play them. He was swinging the bat pretty good tonight."
Guillen said he will continue to hand the ball to Floyd and expects that the hurler will find a way to pitch himself out of his recent rut.
"If you don't have confidence pitching for Ozzie Guillen and Don Cooper, I don't think you're going to find confidence anywhere else," Guillen said. "Because I never made those guys lose confidence. I'm going to give them the ball every time to give them a chance. I'm going to give them at-bats they're supposed to get."
Louie Horvath is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.