Paul Konerko figured this was right about where the White Sox would be. He never envisioned what it would take to get there, though.Konerko hit his 19th home run to snap an eighth-inning tie and the White Sox won their 11th straight game, beating the struggling Cubs 3-2 on Saturday.The White Sox are on their longest win streak since a 12-game run in June 1961, and they can thank Konerko for keeping it going. He broke a 2-all tie with one out in the eighth when he connected off reliever Andrew Cashner (0-1), sending the White Sox to their 15th victory in 16 games.Konerko turned on a 1-2 pitch and the ball reached the left-center seats in a hurry. Fans broke into a “Paulie! Paulie!” chant as he circled the bases, drawing a curtain call from the slugger.The home run made a winner of J.J. Putz (4-2), who pitched a scoreless eighth after Freddy Garcia went seven innings.Matt Thornton worked the ninth for his third save with closer Bobby Jenks tending to an ailing family member, getting Alfonso Soriano to hit into a game-ending double play after Aramis Ramirez walked.The White Sox (39-34) moved five games above .500 for the first time since last July 23 and into a tie for second in the AL Central with Detroit, 1½ games behind Minnesota.But on June 8, when the White Sox were 24-33 and 9½ games out of first after losing to Detroit? The White Sox turnaround has given some hope to the struggling Cubs, but their misery continues.At least there were no tantrums like the one a screaming Carlos Zambrano delivered in Friday’s 6-0 loss, when he had to be separated from teammate Derrek Lee in the dugout and got sent home following a four-run first. The Cubs suspended Zambrano indefinitely, and manager Lou Piniella said Saturday he won’t have a spot in the rotation when he returns.The Cubs got another good start from Carlos Silva and a leadoff homer from the struggling Aramis Ramirez in the top of the seventh that tied it at 2, but lost for the sixth time in eight games.The White Sox got a run-scoring single from Alex Rios in the third, and quickly regained the lead after Lee singled home a run in the sixth on a sacrifice fly by Alexei Ramirez in the bottom half.Aramis Ramirez, in his second game back after missing 15 with a sprained thumb, tied it when he drove a 2-1 pitch from Garcia just over the center-field wall leading off the seventh for his sixth homer, but the Cubs fell to 11-17 in one-run games.Garcia went seven innings, allowing two runs and eight hits, but did not figure in the decision after winning five straight starts. Silva basically matched Garcia, holding the White Sox to two runs and three hits over six innings in another strong start, although he did hit three batters with pitches. Still, the Cubs lost by one again.

NOTES—Guillen expects to have Jenks back on Sunday….The Cubs selected RHP Brian Schlitter from Triple-A Iowa and optioned right-hander Jeff Stevens to the minor league club before the game….The win gives the White Sox the BP Crosstown Cup for taking the season series from the Cubs, but don’t expect them to parade it around town the way the Blackhawks did with the Stanley Cup. “I already tried to give it away,” Konerko said. “It’s kind of cool.” …..If the ‘Hawks hadn’t won the Cup and the thing hadn’t happened with BP — there’s two things working against it.”