Floyd and relievers Matt Thornton and Addison Reed combined to retire the Royals' final 16 batters.
Billy Butler knocked in both runs in the first inning with a two-run single, following David Lough's walk and Alex Gordon's double. That gave Butler 97 RBIs, the most in his career, but his satisfaction was minimal.
"Not much if you don't win," Butler said. "We played well, we started out strong, we just couldn't do anything else."
After that, Floyd spaced out two singles and a double off the wall by Jeff Francoeur. However, Francoeur with his two-out smash to left field in the fourth inning turned out to be the Royals' last baserunner.
"They did a nice job, they retired our last 16 batters," Royals manager Ned Yost said. "We had a hard time centering them up. I think we hit five balls hard all night long. After the first inning, not much offense."
In fact, pitchers on both sides were so efficient that the 14,420 fans saw the Royals' quickest game this season, two hours and 12 minutes.
Alex Rios provided the deciding run in the White Sox seventh when he sent a 3-0 pitch from Hochevar soaring down the left-field line where it landed 423 feet away for his 24th homer.
"A lot of those big home-run guys get the green light 3-0 and I kind of had the gut feeling he was going to, so I tried to step on the gas a little bit and the ball just came up," Hochevar said. "I just left that ball out over the plate and he whacked it."
Hochevar's second pitch of the game was belted into the right-field bullpen by Alejandro De Aza for his eighth home run.
But Hochevar quickly righted himself, retiring the next 10 batters and getting through the fifth with no more damage. Along the way, he got some superb defensive help. Lough made a diving catch of DeWayne Wise's line drive in right-center field to start the third inning. Gordon began the fifth by fielding A.J. Pierzynski's hit down the left-field line and throwing him out at second base.
"Our defense has been solid all year long and that's just another example of it," Yost said.
Hochevar's serenity ended in the sixth when Gordon Beckham opened the inning with a home run, a drive into the left-field seats. It was Beckham's 16th blast and created a 2-2 tie.
All three home runs came on fastballs.
"I felt like the one to De Aza, I was trying to go belt in and I got in there and he put a good swing on it," Hochevar said. "And the one to Beckham was supposed to be a fastball down and away and it just ran back over the middle."
As Yost pointed out, giving up three runs in seven innings constitutes a good outing for a starter and Beckham agreed that Hochevar was solid.
"He did a really good job tonight, one of the best I've seen him," Beckham said. "He was good. He just left a couple mistakes over the plate. Tough luck for him. Sometimes you throw those pitches and they don't get hit out. It's just bad luck, I guess."
The White Sox had a chance to do more damage against the Royals' bullpen in the eighth inning. Left-hander Tim Collins issued a two-out walk and right-hander Louis Coleman was summoned to face righties Paul Konerko and Rios. But Coleman walked both of them to load the bases.
That brought lefty Francisley Bueno into the game and he got Pierzynski to ground out. Bueno has a clean slate so far with inherited runners, stranding all 11 he's had this season.
"Bueno did a real nice job," Yost said. "You get in that situation and bring in a reliever, you don't want him walking the next two guys. So Bueno picked us up nicely there."
But it was Floyd, making his second start after coming off the disabled list with an elbow strain, who carried the most impressive load on the mound. Butler gave him credit.
"He came back off the DL this last time and he's throwing harder," Butler said. "I saw him in the mid-90s, hitting 94 quite a few times. His slider was 86, 88 and I hadn't seen that from him. It broke late and, out of the hand, I thought it was a fastball. He's always had one of the better sliders I faced and when you throw it shorter like that and breaking late, it's going to be tough and that's what he was tonight."
Except for the rocky beginning, Floyd was pleased.
"They are a good hitting ballclub. I know that they're aggressive," Floyd said. "But I'm just trying to make my pitch, and most of the time that'll get the guys out."
After that first inning, it certainly did.