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5/13/2014 10:24 P.M. ET

Eaton ready to start Minor League rehab assignment

OAKLAND -- Rehabbing outfielder Adam Eaton ran sprints and tested out his right hamstring before Tuesday's contest against the A's.

Starting Wednesday, he'll be jet-setting all over the country as he tries to get some game action with Triple-A Charlotte. His itinerary for the upcoming week is hectic to say the least.

"Should be fun," Eaton said. "Basically touching both sides of the United States in one fell swoop."

Eaton will work out at O.Co Coliseum on Wednesday morning and then travel to Durham, N.C., to play two games with the Knights on Thursday and Friday before taking a bus to Norfolk, Va., for four more innings on Saturday. If all goes according to plan, he'll join his White Sox teammates in Houston on Sunday -- the first day he's eligible to return from the 15-day disabled list -- for the series finale, before jumping on another plane to Kansas City as the road trip continues.

"Excited to get back Sunday," Eaton said. "It's no fun being on the dead list. … It's definitely playable right now, and we'll find out more when we actually get to games. Once adrenaline gets going, you're pushing it a little bit further. I would say I'm ready to go."

Acquired in the offseason from Arizona, Eaton has taken up the team's starting center fielder and leadoff roles when healthy. In 25 games before his injury, Eaton was batting .276/.363/.378 with a homer, 14 RBIs, 11 walks and 16 strikeouts.

"It's kind of easy hitting on top of this order," Eaton said. "With [Jose] Abreu, [Paul] Konerko going against lefties and [Adam] Dunn going against righties. Some very, very good hitters with a lot of pop behind you. It's a fun lineup to be in."

Abreu expected to get consecutive days off this week

OAKLAND -- Slugging first baseman Jose Abreu has been relegated to designated hitter as he works through a left ankle injury. In order to give Abreu a bigger break, White Sox manager Robin Ventura said he plans on using Thursday's off-day to give Abreu consecutive days off.

"I don't know if we're going to do it either [Wednesday] or [Friday], we'll see how he goes through today," Ventura said before Tuesday's contest against the A's. "But I'm sure one of them he'll get [off]."

Chicago wraps up the series in Oakland on Wednesday before heading to Houston for a three-game set this weekend.

Abreu has been dealing with foot and ankle issues since Spring Training, but showed a noticeable limp while trying to run down to first base on Thursday against the Cubs. He's been the starting designated hitter in the five games since. The 27-year-old has started every contest this season except for April 17, when he made a pinch-hitting appearance.

"It's getting better," Ventura said. "There's nothing structurally or anything you're concerned about. But you just see him limp like that and it's just soreness getting out of there. It's getting better. I think that day off will probably help."

Abreu belted his Major League-leading 14th home run during Monday's ninth-inning comeback, which came up a run short. He took A's starter Jesse Chavez deep to right field for a solo shot on a line drive that got out of the park quickly.

"He has a lot of power," Ventura said. "You see him hit balls -- the way they come off the bat is just different than a lot of people. He has power to all fields. Any park you play in is reachable for him, anywhere. He puts it on the barrel and good stuff happens."

Ninth-inning production leads the Majors

OAKLAND -- The White Sox scored three runs in the ninth inning on Monday night against some of Oakland's top bullpen arms, but still came up short in a 5-4 loss.

Jose Abreu started the rally against A's starter Jesse Chavez by hitting a solo shot to right, ending a streak of 10 straight retired batters by Chavez. Then the next three batters reached base against Jim Johnson and Sean Doolittle before Paul Konerko hit a sacrifice fly to make it 5-4.

Though they lost the game, the White Sox were able extend their Major League lead in ninth-inning runs scored to 38, which is far ahead of the second-place A's (23). Chicago also is tied for second in ninth-inning batting average (.293) and second in on-base percentage (.391) during the frame.

The White Sox have already put together some memorable walk-off wins as part of their 10 comeback victories.

"One thing is to have the feeling that you're going to do it," manager Robin Ventura said, "and the other thing is having done it already a couple of times this year. You build momentum off of that."

The numbers stand in stark contrast to last season, when the White Sox batted just .228 with 45 runs scored during the ninth.

"It's definitely a different feel offensively compared to what we've seen in the past," Ventura said. "These guys are grinding stuff out and it'll happen every once in a while."

Lineup stacked with righties against A's left-hander

OAKLAND -- White Sox skipper Robin Ventura stacked his lineup against A's lefty Drew Pomeranz with eight righties and switch-hitting Leury Garcia on Tuesday night. Heading into the contest, Chicago was 5-5 against southpaw starters and 14-16 against righties.

Outfielder Alejandro De Aza was noticeably absent from the batting order as he continues to scuffle at the plate. Through Monday's action, De Aza's .180 batting average was the eighth lowest in MLB, while he had 36 strikeouts and nine walks in 39 games.

"He's just swinging and missing at a lot of stuff, working at-bats and such," Ventura said. "I think he just needs a day [off]."

The team's hottest hitter lately has been second baseman Gordon Beckham, who batted .343 (12-for-35) with a double, two homers and five RBIs during his eight-game hit streak entering play Tuesday. Ventura said Beckham has benefited from a stronger lineup in 2014 after he appeared to be pressing at times during his 2013 campaign.

"When other guys are contributing, it's easier to kind of stay in your lane and do what you do best," Ventura said. "That's what he's doing."

Third to first

• Once again on Monday night, the White Sox lineup featured a quartet of Cubans in Abreu, Dayan Viciedo, Alexei Ramirez and Adrian Nieto. According to A's Spanish radio broadcaster Amaury Pi-Gonzalez, the 2014 White Sox are the first team to start four Cubans in the same lineup since the 1969 Cleveland Indians, which featured Jose Cardenal, Joe Azcue, Zoilo Versalles and Luis Tiant.

• Before Tuesday night's contest in Oakland, A's slugger Yoenis Cespedes poked his head into the White Sox clubhouse before trading bats with Viciedo.

Alex Espinoza is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.