Eloy Jiménez had a run-scoring double for AL Central-leading Chicago, which earned its third consecutive victory.
Seth Brown homered for Oakland, which lost its fourth straight. Paul Blackburn (0-1) allowed three runs in 5 1/3 innings.
The A's learned before the game that pitcher Chris Bassitt has a broken bone in his cheek and needs surgery. The right-hander sustained no eye damage after being struck on the side of the head by a line drive Tuesday.
General manager David Forst said it's too soon to project whether Bassitt will pitch again this season or how long it could take him to return.
Robert and Jiménez are back after being sidelined by injuries, adding depth to Chicago's lineup.
The 24-year-old Robert is 12 for 28 with six RBI in seven games after missing three months with a hip flexor strain. Jiménez is hitting .319 with six homers and 21 RBI in 18 games since coming back on July 26 from a pectoral tear that had sidelined him since spring training.
Manager Tony La Russa credits both with diligence during minor-league rehab stints that has carried over.
"What's really impressive is that they worked hard to get here sooner than we expected," La Russa said "But when you work hard as they worked and you've got talent like they have, then you shouldn't be surprised."
Robert slipped trying to catch Elvis Andrus' triple in the seventh, and Andrus scored on Starling Marte's sacrifice fly.
Other than that, Robert said he's doing fine.
"I'm not 100%, but the percent I'm playing now I can help the team," the Gold Glove center fielder said through a translator. "I'm feeling stronger every day."
Garrett Crochet (3-5), the first of four White Sox relievers, pitched 1 2/3 innings for the win. Liam Hendriks got five outs for his 28th save, striking out the side in the ninth against his former team.
Craig Kimbrel, used as a setup man since coming over from the Cubs at the trade deadline, wasn't available because he was in Alabama following the death of his grandfather.
White Sox starter Lance Lynn was ejected by third-base umpire Nic Lentz in the middle of the fourth when he complained and threw his belt during a foreign substance check at the dugout. The big right-hander allowed one run and three hits while laboring through 88 pitches.
Lynn said Lentz came late to the dugout and while he was trying to get attention from the training staff before going back out.
"Obviously I hurt his feelings," Lynn said. "He threw me out because I threw my belt. I said, 'If you were on time, we wouldn't have this problem.'"
Blackburn (0-1) permitted five hits, struck out three and walked three in his first major league appearance this season after being called up to take Bassitt's roster spot. Oakland's other starters were pushed back a day.
Blackburn said he learned that he was starting at about 3:30 p.m.
"I thought he did great," manager Bob Melvin said. "I thought after giving up a couple of hard-hit balls in the first, he pitched really well to get us to the sixth and have us within a run."
Bassitt was taken to the hospital after getting hit by a ball off Brian Goodwin's bat in the second inning of Tuesday's 9-0 White Sox win. The 32-year-old has shown no signs of a concussion and a scan of his brain was normal, following an ordeal that left him crumpled and bleeding on the mound.
Oakland fell one game behind New York for the top AL wild card. The Yankees are 69-52, followed by the A's at 68-53 and the Red Sox at 69-54.
Lynn's pitch count soared as he escaped jams in the first and third without allowing a run.
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While still concerned for Bassitt, Melvin said his team was relieved to learn the righty should recover.
"We got what we considered was good news today so everybody's in much better spirits in the clubhouse today," Melvin said. "You have to go through certain events in your career, this being on the extreme end, but it's just going out there and trying to win today's game."
Hendriks said he was hit hard by the Yankees in two appearances in the previous series because he was tipping his pitches. The All-Star allowed seven runs and five hits - including three homers - in 1 1/3 innings against New York.
"Tipping is the easiest thing to fix," Hendriks said.
Hendriks said his wife, Kristi, had noticed it - even before he reviewed videos.
"She's always right," Hendriks said.
Athletics: Bassitt was placed on the 10-day IL.
Oakland LHP Cole Irvin (8-11, 3.52 ERA) faces Chicago RHP Dylan Cease (9-6, 4.04 ERA) in the series finale on Thursday.
Lance Lynn ejected after tossing belt at umpire during foreign-substance check
During a foreign-substance check, White Sox pitcher Lance Lynn tosses his belt at an umpire and is promptly ejected.