Zach Remillard added a two-run single and Eloy Jiménez had a pair of RBI singles as the White Sox finished their seven-game road trip 3-4.
"We needed that one today," Burger said. “I’m glad that we got the job done.”
Brent Rooker homered for Oakland hours after being named an All-Star.
Chicago jumped on A’s starter Paul Blackburn for five runs in the third inning. Tim Anderson started the scoring with a sacrifice fly, followed by Jiménez’s first RBI single.
Gavin Sheets was hit by a pitch with the bases loaded to force in a third run and Remillard singled home two more to make it 5-0.
Blackburn (1-1) gave up five runs on six hits in five innings, striking out five and walking four.
“I really feel like he was fighting himself all day,” A's manager Mark Kotsay said. “He didn’t have his best command. He just couldn’t get the breaking ball where he wanted. The changeup wasn’t real effective. Grinding through those five innings, it wasn’t easy for him, but he walked off the mound, we still had a chance to win that game.”
Oakland got two runs back in the bottom of the third on an RBI single by Tony Kemp and a bases-loaded walk by Seth Brown.
JJ Bleday doubled home a run in the fifth to make it 5-3.
Andrew Benintendi had a sacrifice fly in the sixth, followed by Jiménez’s second RBI single. Burger homered 442 feet to center in the seventh.
“Been going through it for a couple of weeks now, so it was good to kind of feel myself today,” Burger said. “I felt exactly like myself, what I was feeling about a month ago.”
Rooker hit a two-run homer 441 feet to center in the eighth.
Bleday added another RBI double in the ninth, followed by an RBI single by Brown to bring the A’s within 1. But Gregory Santos got Jace Peterson to line out to right, earning his first career save.
"Today we needed every single run," White Sox manager Pedro Grifol said. “We needed every single at-bat. We needed every single pitch to get this one.”
Touki Toussaint made his third appearance and first start for the White Sox, allowing two runs and three hits in 3 2/3 innings. He struck out five and walked four in a no-decision.
Aaron Bummer (3-1) was credited with the win, allowing a run in 2 1/3 innings with two strikeouts.
“He saved us today,” Grifol praised. “He had really good stuff. He used his slider, his fastball and his sinker. He did a really good job.”
The Athletics were seeking their second sweep of the season but finished their six-game homestand 3-3.
Before the game, A’s backup catcher Carlos Pérez and his brother of the same name, White Sox backup catcher Carlos Pérez, caught ceremonial first pitches from the Oakland catcher’s two children, Marcela and Mateo.
Rooker and White Sox OF Luis Robert Jr. were each selected to their first All-Star Game. Rooker leads Oakland with 14 home runs and 41 RBIs. He is batting .243 with an .816 OPS in 72 games.
Robert ranks second in the American League with 24 homers. He leads Chicago with a .912 OPS, batting .276 with 46 RBIs in 83 games.
White Sox: Placed RHP Michael Kopech on the 15-day injured list, retroactive to June 29, with right shoulder inflammation. Chicago selected RHP Bryan Shaw from Triple-A Charlotte and transferred INF Romy Gonzalez (right shoulder inflammation) to the 60-day IL.
Athletics: Reinstated LHP Richard Lovelady (strained left elbow) from the 15-day IL and optioned LHP Kyle Muller to Triple-A Las Vegas.
White Sox: RHP Lucas Giolito (6-5, 3.53 ERA) opens a three-game home series against Toronto on Tuesday night. The Blue Jays counter with RHP Chris Bassitt (8-5, 4.06), who began his career with the White Sox in 2014.
Athletics: LHP JP Sears (1-6, 4.43) tries to snap a three-game losing streak Tuesday night when Oakland opens a three-game series in Detroit. The Tigers hadn’t announced a starter.
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