Boston will need a strong second-half to make a run at the Yankees in the American League East or at a Wild Card spot in a league that entered Monday with 11 teams better than .500.
Chicago, meanwhile, will need to continue its unexpected success to hold off hard-charging Detroit, which has won eight of its last nine games and is only 2 1/2 games out in the AL Central.
"We expected [Detroit] to play well at some point," White Sox catcher A.J. Pierzynski said. "As long as we continue to play well and do our thing, it doesn't matter what anyone else does. We'll take care of our own business. It will all work out in the end as long as we continue to do our job.
"You worry about things out of your control. We should worry about what we can control."
What the White Sox can control is their matchup in Boston on Tuesday, when the team will call on right-hander Philip Humber, who has been on the disabled list since June 17 because of a strained right elbow.
Humber appeared in a rehab game for Double-A Birmingham on Thursday, allowing one run on two hits and no walks in six innings.
His Major League outings haven't gone nearly as smoothly -- Humber is 3-4 with a 6.01 ERA this season. Since his perfect game on April 21, his ERA is 7.47.
Boston starter Jon Lester's first half wasn't much better, as he went 5-6 with a 4.49 ERA and was admittedly upset with his performance.
The left-hander closed his poor first half on a low note, allowing five runs (four earned) on nine hits in 4 1/3 innings to take a loss against the Yankees on July 8.
"Uncharted water for me," Lester said. "I've just got to keep grinding it out. I can't give up, I've just got to keep working. That's all I can control. Just keep showing up every day and working hard, and things are going to turn around."
Lester got a reprieve from the grind during the All-Star break, and he's hoping that time away will lead to a turnaround.
"It's a good mental break to get away from it for a couple days, get out of the monotony of the same routine I do every day," Lester said. "It will be good to relax and not worry about bullpens or anything like that."
All both teams want to worry about is their next game, regardless of how the standings look.
"Sometimes you get caught up in looking at the big picture instead of focusing on yourself and what you need to do," Pierzynski said. "That's when you get into trouble."
White Sox: Floyd to disabled list
Right-hander Gavin Floyd was placed on the 15-day disabled list Tuesday because of tendinitis in his right elbow. An MRI on Sunday showed no structural damage.
Floyd, 7-8 with a 4.54 ERA in 17 starts, had never been on a disabled list in his 11-year professional career.
Alexei Ramirez snapped a nine-game hitting streak with his 0-for-3 performance on Monday night.
The White Sox entered Monday tops in the Majors with a .297 average with runners in scoring position, but they are just 11-for-63 in their last six games.
Alejandro De Aza is 4-for-36 in his last eight games.
Red Sox: Two steps forward, one step back
Manager Bobby Valentine said David Ortiz could be out for a "few days" because of a right Achilles injury the designated hitter sustained running the bases on Monday, putting a damper on a Red Sox lineup that had seen an uptick in health since the All-Star break.
After missing the entire first half of 2012 with wrist and elbow injuries, Carl Crawford returned on Monday and singled up the middle in his first at-bat.
Adrian Gonzalez is recovered from back spasms that kept him out of the lineup on Friday and Saturday, Jacoby Ellsbury returned on Friday after a three-month stint on the disabled list due to a separated right shoulder and Dustin Pedroia is likely to return from a right thumb strain on Thursday.
Ortiz went 1-for-3 on Monday, notching a hit and a walk for the 10th straight game to break a franchise record previously held by Ted Williams. He is scheduled to undergo an MRI on Tuesday.
Pedro Ciriaco has recorded three or more hits in four of his seven games this season.
Boston lost 11 of its first 15 home games, but has since won 19 of its 32 games at Fenway Park.
Alex Rios is hitting .222 (8-for-36) with nine strikeouts in his career against Lester.
Boston's 5-1 win on Monday snapped Chicago's seven-game winning streak at Fenway Park. The Red Sox are up 4-1 in the season series, securing at least a split for the first time since 2009. Boston leads the all-time series 960-924, including 552-388 at home.
Humber is 1-2 with a 8.83 ERA (17 ER/17 1/3 IP) in three career starts against Boston.