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6/28/2014 6:34 P.M. ET

Eaton back in lineup after resting legs

TORONTO -- Adam Eaton was back in the lineup after missing Friday's game with leg soreness. The White Sox leadoff man left the series opener on Thursday vs. the Blue Jays in the first inning after he tried to beat out a grounder to second.

Eaton went 1-for-4 with a run scored after legging out an infield single in the eighth inning of Saturday's 4-3 win over the Blue Jays. After spending time on the 15-day disabled list in May with a strained right hamstring, Eaton said the wear and tear on his legs got to a point where he needed some rest.

"Given a day, I felt like they took a sigh of relief, a deep breath and I'm able to get back out there today," Eaton said. "... Probably continue to deal with it. Not out of the woods for sure, but hope to fix it in the next couple of weeks. "

White Sox new closer committee saves win

TORONTO -- The White Sox moved to a closer committee after Ronald Belisario was unable to close out Friday's game in the ninth inning with a three-run lead.

The right-hander gave up a pinch-hit homer to Colby Rasmus before putting two runners on as the Blue Jays threatened late in the game. The White Sox held on for a 5-4 victory after Eric Surkamp and Jake Petricka came on to work through a bases-loaded jam.

Manager Robin Ventura said Saturday that closer duties will fall to the bullpen as a whole going forward.

"It's not ideal," Ventura said. "Right now we're at the point where we thought Beli would be able to do it and it didn't work. At this point, we'll use who we need to use that night."

In Saturday's 4-3 win over Toronto, the White Sox used three relievers to finish off Chris Sale's seventh win. Zach Putnam earned the save after staving off another Blue Jays rally, allowing an earned run on three hits in 1 1/3 innings. After giving up a run on back-to-back hits in the ninth, Putnam was able to retire the top of Toronto's lineup in order to earn his first big league save.

"It's just helping each other, picking each other up," Putnam said. "We have one guy in the 'pen who has some experience and the rest of us would be new to it. There haven't been any conversations [with coaches] about it. I assume it'll be based on freshness, our guys' stuff versus who's coming up."

Belisario blew his fourth save on Monday and has seen his ERA balloon to 7.36 over 7 1/3 innings pitched for the month of June.

He's been unable to convert three save opportunities since taking over the closer role after Matt Lindstrom went down with an injury last month.

"We don't really have [a closer]," Ventura said. "We're going to use whoever we need to use, depending on situation, matchups, usage, whatever it is. We're at the point we're going to use who we think fits best in that spot."

ASG candidate Alexei gets off-day

TORONTO -- Alexei Ramirez was given a day off Saturday because of fatigue, said manager Robin Ventura.

The 32-year-old had a two-run home run in the White Sox 5-4 win over the Blue Jays on Friday, but Ventura noticed some sluggishness from his shortstop, so he opted to give him some rest. Leury Garcia took his place in the lineup.

"He looked tired on the turf," Ventura said. "You see what happened to Eaton a few days ago. He just looked tired, a certain tiredness to him. Give him a day off, then we play four in a row."

Ramirez did not get the whole day off, however, as he came in as a pinch-hitter in the eighth inning and delivered a crucial RBI single in his only at-bat of the day.

The Cuban native is still vying for a spot on the American League roster for the upcoming All-Star Game. He's currently second in AL balloting for shortstops, trailing only Derek Jeter. If successful, Ramirez would become the first White Sox shortstop to make the All-Star Game since Ozzie Guillen in 1991. As of the last balloting update for the American League voting, he had amassed 1,933,117 votes.

He's reached base safely in 67 games this season, tied for third-most in the AL. He ranks first in hits among AL shortstops (92), is tied for first with eight home runs, and is second in both average (.293) and RBIs (38).

Fans can cast their votes for starters at MLB.com -- online or on a mobile device -- using the 2014 All-Star Game MLB.com Ballot Sponsored by Experian until Thursday, July 3, at 10:59 p.m. CT. The 2014 All-Star Game will be played at Target Field on Tuesday, July 15 on FOX.

Jamie Ross is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.