That string of success is in serious trouble after the Royals romped to a 9-1 victory Saturday night and the Twins trampled the Rangers.
The Sox lead is a half-game, its smallest since June 26, when they reeled off five straight victories, and by the time Sunday is over they could be in second place.
"I only worry about Kansas City [Sunday], I can't worry about anybody else," manager Ozzie Guillen said. "You have to take care of your own problems before you take care of your neighbors."
Guillen's thoughts were echoed in the clubhouse, where captain Paul Konerko said he expected the Central race to go down to the end and have a lot of momentum swings.
"There are going to be hot and cold streaks," he said. "You want to get all the wins you can, but it's not that time yet where you scoreboard-watch."
The scoreboard showed only two hits for the Sox against Gil Meche and three relievers and, in the end, showed only the second loss in eight games against the Royals.
Saturday's defeat also was only their third in the last 15 games played at U.S. Cellular Field, where 36,566 disgruntled fans watched.
The Sox hitters never got on track, a rarity at home, where they had batted .304 and averaged seven runs per game over the last 24.
"That's as good as we've seen Meche," said Konerko, who was 0-for-3.
Sox starter Gavin Floyd (10-6), coming off his shortest outing and his career-worst seven walks in Texas, lasted six innings and became the victim of his own pitch count. It took 100 pitches for him to get through six, even though he allowed only four hits and had only one inning when the Royals scored.
Joe Crede's 19th error, to open the fifth inning, led to three runs. John Buck followed the error with a homer, then Joey Gathright singled, stole second and scored on Billy Butler's single.
"I got in a little trouble and got out of it with a minimum amount of damage," Floyd said. "The other pitcher pitched real well."
Meche, who had given up 26 hits over his last three outings, didn't give up a hit to the Sox until Crede's double in the third inning, and he made it through 62/3 innings surrendering only two hits.
In the eighth, the Royals beat up on relievers Boone Logan, Nick Masset and Adam Russell. The three combined to give up six runs on five hits, two walks and a wild pitch. All three batters Masset faced came in to score.
"We need those guys to contribute better," Guillen said.
The Sox are in danger of falling out of first place for the first time in more than two months.
"We just have to play our game," Floyd said. "What [the Twins] do is out of our control."