"You just always try to win series back to back and keep winning series, especially when you haven't won a lot," Cubs manager Dale Sveum said. "If you keep winning series, you can gradually get back into this thing in some kind of fashion anyway."
Wells (1-2) got the start as a sub for Ryan Dempster, who was placed on the disabled list on Monday. It was the right-hander's third start with the big league team and first since April 28. He had opened the season at Triple-A Iowa despite a strong showing in Spring Training.
"He's been fighting to get back," Sveum said.
Wells walked a batter in each of the first two innings, but avoided trouble both times. That changed in the third. Eduardo Escobar walked, then stole second, and Alejandro De Aza walked, with both runners advancing on Beckham's sacrifice. Adam Dunn and Paul Konerko each hit RBI singles to open a 2-0 lead.
With one out in the White Sox fourth, Alexei Ramirez singled. One out later, De Aza reached on an infield single to shortstop Starlin Castro, who tried to flip to second baseman Darwin Barney for the force, but missed. Beckham then dropped a single past a diving Barney in shallow right, scoring Ramirez. Wells was pulled after giving up three runs on five hits and four walks over 3 2/3 innings.
"The four walks are unacceptable," Wells said. "I won't accept it. They shouldn't accept it. I don't know what's going to come after that. If I do get another one, it's time to go back to the drawing board and really focus on pounding fastballs down and away and get back to the basics, so to speak."
The Cubs could recall Chris Volstad, who was sent down to Iowa after opening the season 0-6 in eight starts, or they could bring up lefty Chris Rusin, who was 5-5 with a 4.56 ERA in 14 starts, but had two starts in which he threw eight shutout innings.
"We'll weigh our options," Sveum said.
Volstad, acquired from the Marlins for Carlos Zambrano, is 2-1 with a 4.78 ERA in six starts at Iowa.
"He hasn't been pitching all that good except his last outing," Sveum said. "Hopefully he's getting going and building a lot of confidence. I think a lot of it with him is just confidence."
Floyd (5-7) came into the game with one win in his last six starts, and had given up 35 runs over 30 1/3 innings, but the Cubs couldn't muster much. He held them to four hits while striking out four over 6 1/3 innings. They had chances. David DeJesus doubled to open the Cubs third, and was stranded.
"We gave one away where we could've taken the lead early if we got the guy over and we swing at the first pitch and roll over and don't get anything out of that," Sveum said of Castro's at-bat after DeJesus' hit. "That was probably the key of the game right there."
Castro did triple to open the sixth, and Floyd was able to retire the next three hitters.
"We've got to bear down and figure out a way to get those guys in, whether they're giving us a run by playing the infield back, especially in those situations," Reed Johnson said. "We've got to get a ball over the plate and use the whole field. Hopefully we can clean those things up. Situational hitting is something we have to work on."
Beckham homered with one out and two on in the sixth off lefty Scott Maine to open a 6-0 lead.
"I don't think that put the game away," Beckham said. "The Cubs have been playing really well, and they've shown it the last couple days. It put some distance between us, which was good. That's all it was. We still had three innings left, so by far it wasn't the end of the game."
The Cubs return to National League play this weekend against the Arizona Diamondbacks. They had a long flight to Phoenix after Wednesday's game to think about the series and the season.
"This one leaves a bad taste in my mouth," Wells said. "I felt good, came out early throwing strikes and got a lot of ground balls early. I don't know if it was the walks or pitching timid to guys like Dunn and Konerko, and some things could've gone either way, but like I said, any time you walk four guys in 3 2/3 innings, you're not giving yourself a very good chance."