"It was a good run," first baseman Paul Konerko said. "It was good to see the fight at the end of the game. They were just a little bit better in all areas in the game. You have to tip your hat to Ryan Dempster. He pitched a great game."
Tyler Colvin and Alfonso Soriano homered for the Cubs. The Cubs led 6-2 after the top of the sixth and a weekend that began with Carlos Zambrano's dugout tantrum and indefinite suspension ended on a positive note for a team still far below .500.
"We've got to be professional," Soriano said. "Whatever happens outside is part of the game. We're here to play every day."
Konerko hit his 20th homer for the White Sox, tying Frank Thomas' club record with 11 seasons of 20 or more.
Down 8-3, the White Sox started to come back when Marmol walked Mark Kotsay and A.J. Pierzynski with one out. After Alexei Ramirez flied out, Gordon Beckham hit an RBI double and Juan Pierre followed with a two-run single. Pinch-hitter Andruw Jones walked before Rios struck out.
"Well, it was enjoyable," manager Ozzie Guillen said. "We enjoyed it a lot. I think the guys are having more fun now and they believe we can keep playing like this."
Colvin's three-run shot off John Danks (7-6) in the third gave the Cubs a 3-2 lead and Derrek Lee extended it with a two-run double in the fifth,
Soriano led off a two-run eighth with his 11th homer, connecting against Tony Pena. And after the White Sox came up short in the ninth, the Cubs could finally exhale after a chaotic weekend.
Three years ago, they turned things around and went on the win the NL Central after Zambrano fought in the dugout and clubhouse with former catcher Michael Barrett and manager Lou Piniella got ejected in back-to-back games against Atlanta.
"I don't think it's because of the Zambrano incident that we win today," Aramis Ramirez said. "I don't think we're going to get hot because of it. No team wants to go through that."