Konerko homered off Cubs starter Rich Hill in the first inning and John Webb in the fifth. Dye sparked a four-run White Sox fourth with his three-run drive off reliever Juan Mateo. Rob Mackowiak hit a solo homer against Mateo later in the inning.Derrek Lee hit his first homer of the spring for the Cubs, who dropped to 0-3 in Cactus League play.White Sox right-hander Jon Garland pitched three scoreless innings. He allowed two hits, walked one and struck out one.Konerko's homers were his first two of the spring."Usually I start out OK and then have a little dip somewhere in the middle and get worried and work harder," he said. "But the last week (of spring), and more specifically the last couple of games, is when you get the feel."Dye's three-run drive to left was his second of the spring."Like Paulie said, it's just about getting feel and getting to see different pitches," Dye said. "The results are good sometimes and sometimes they're bad. That's why you have spring training."Konerko opened the scoring with two outs in the first inning. Hill, a lefty, struck out Brian Anderson and Robert Valido to start the game before giving up Konerko's homer."Just that one pitch, I kind of left it over the middle of the plate," Hill said.The homers by Dye and Mackowiak gave the White Sox a 5-0 lead in the fourth. In the bottom of the inning, Lee led off with his homer.The game was played before 12,903 fans, a record for HoHoKam Park.The White Sox improved to 2-4 this spring.