"I'd never faced him before," Lee said after his three hits and four RBIs helped Chicago to a 7-2 victory over Appier and the Oakland Athletics on Sunday.
"You have to come to the park the same way no matter who is pitching. I take the same approach all the time. And once you get in a streak, you don't want to do too much. Just keep swinging the same way."
James Baldwin (9-11) allowed seven hits and two runs in six innings with three walks and seven strikeouts to win his fifth straight decision.
And reliever Keith Foulke, who posed for pregame pictures with his dog Shep as part of the White Sox's Dog Day of August promotion, got his seventh save. He pitched out of a one-out, bases-loaded situation in the eighth and threw a doggone perfect ninth.
"Dog care means a lot," Foulke said. "But that's not what I'm out there pitching for."
Appier, meanwhile, has lost three straight after winning his first three for the A's.
He entered the game 4-0 against the White Sox this season, including three victories before he was traded by Kansas City on July 31, but was hurt by his own wildness and two infield hits by the White Sox. He allowed eight hits and seven runs with six walks in four-plus innings.
He said a strain in his upper right leg has been affecting his pitching.
"The leg's beean issue. Today I did feel better, but I was having trouble driving through some balls," Appier said.
"In compensating for it, it was making me do some weird stuff with my upper body. Today, it just kind of held me back from getting clean to my target."
Lee hit a two-run, bases-loaded single in the fifth and a third run scored on the play when Oakland center fielder Rich Becker overthrew third. That gave the White Sox a 6-2 lead and finished Appier (12-12).
"He threw me some off-speed pitches and I stayed back and drove it through the middle," said Lee, who is 14-for-29 with 14 RBIs over the last seven games.
Moments after his hit, Lee slid home with the fourth run of the inning as Greg Norton's slow roller crawled up the first base line for a single.
Lee was cut down at the plate by second baseman Randy Velarde while trying to score on Norton's double.
Stairs singled in the third and scored on Ben Grieve's double for a 2-1 lead.
But Appier walked Ray Durham and Frank Thomas in the bottom half and Magglio Ordonez hit an RBI double. Paul Konerko also walked to load the bases and Chicago went up 3-2 when Lee's two-out, topped roller down the third-base line stayed fair for an infield single.
The A's loaded the bases in the eighth before Foulke got Becker on a comebacker which he threw to the plate for a force and then retired Velarde on a fly ball.
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