The victory, coupled with Minnesota's 11-1 loss at Tampa Bay, gave the White Sox a 2 1/2-game lead over the Twins in the American League Central. The loss snapped the Royals' seven-game winning streak, their longest since starting the 2003 season 9-0.
The White Sox sent 10 men to the plate in a six-run fourth inning, scoring all the runs with two outs.
Jermaine Dye doubled, Jim Thome singled and A.J. Pierzynski walked before Ramirez tied the rookie record with his third grand slam. Shane Spencer hit three grand slams as a rookie for the New York Yankees in 1998. Ramirez fouled off six pitches from Bannister, including four with two strikes, before hitting the slam.
"That was an unbelievable at-bat," White Sox manager Ozzie Guillen said. "He fouled off a lot of pitches. We needed that. We struggled in the New York series and then we score six in one inning, everything came after two outs and two strikes, and we feel a little better about the game."
It was Chicago's 11th grand slam this season, tying the club record set in 2006.
"I didn't go up there to hit a home run, but put the ball in play," Ramirez said through an interpreter. "I was studying what pitches he had in my first at-bat. The second at-bat after having two strikes, I knew kind of what he might come with and the pitch stayed in the zone and I saw it really well, swung at it and fortunately it was a home run."
Pierzynski had his own nine pitch at-bat before drawing a walk.
"I just kept throwing strikes and they kept fouling them off," Bannister said. "I was one strike away and kept throwing strikes. They fouled them off and I kept trying to be aggressive. Pierzynski had a tough at-bat, fouling off a lot of pitches, and Ramirez did, too.
"Alexei kind of threw his bat at the ball. He got out in front of it. He did a good job of keeping that ball fair."
Thome hit his 33rd homer in the fifth off Bannister (8-16).
Buehrle (14-11), working on three days' rest, gave up three runs and six hits. He is 3-0 in four September starts and is 6-1 in his past nine starts.
"I forget about being on short rest until I came in," Buehrle said. "I didn't feel too good in the bullpen and somebody asked me if it was because of three days' rest. Once I got on the mound, it was one of the better games I felt. It seemed liked I was wild and falling behind. It didn't seem like everything was working, but it's one of those games that I felt good and had to battle through."
Bannister retired eight of the first nine hitters he faced before allowing six runs on six hits, a walk and a wild pitch in the fourth. Bannister, who left after allowing seven runs and eight hits in five innings, is tied for the American League lead in losses. He has one win in 15 starts since a June 23 victory over Colorado. Bannister, who has given up eight home runs in four starts against the White Sox this season, has allowed 29 home runs, second in the AL.
"Everyone knows they live by the home run and that's tough since I'm a fly ball pitcher," Bannister said.
Said Royals manager Trey Hillman, "If we could take away that fourth it would be a different game. That inning just snowballed on him."
"Ever since Teahen's been back from being sent down to the minors a couple of years ago, I haven't been able to get him out," Buehrle said. "I think I've thrown him every pitch I have and he's that good of a hitter now."
Tejeda left with a strained left hip flexor after throwing a wild pitch in the seventh. ... The White Sox have hit four or more home runs in a game 11 times, tops the majors.