The loss extended the losing streak for A's starter Chris Bassitt (0-3) to nine games, a streak that dates back to August 2015. He allowed five runs (four earned) in 5 1/3 innings. The right-hander has a 5.55 ERA in 13 starts during that stretch.
"I thought [Bassitt] was better; I really did," A's manager Bob Melvin said. "Other than the one inning, I thought he threw the ball really well. He mixed speeds really well and had a really good curveball.
Some of the runs came after he left the game, but other than the second inning, he pitched really well."
Matt Olson had a home run and two RBIs to pace Oakland.
Lucas Giolito (5-7) allowed four runs on seven hits in seven-plus innings for the win. Tim Anderson homered and Omar Narvaez and Adam Engel each drove in a pair of runs as the White Sox snapped an eight-game losing streak.
After winning Game 1, 11-2, the A's jumped on top with a run in the first. Matt Joyce and Khris Davis drew back-to-back two-out walks, and Olson followed with a single to left to drive in Joyce for a 1-0 lead.
After retiring the first four batters, Bassitt allowed hits to four of the next five batters in the second. Narvaez gave the White Sox a 2-1 lead with a two-run single, and Charlie Tilson added a run-scoring single with two out to make it 3-1.
Olson's solo shot in the sixth pulled the A's to within 3-2. The blast also pushed the A's road homer streak to 23 games, extending the franchise record. The Major League record is 24 games, set by the Baltimore Orioles in 1996.
The momentum was short-lived, though, as the White Sox answered with a pair of runs in the bottom of the sixth -- aided by an error.
Matt Davidson led off the frame with a walk. One out later, Anderson hit a grounder to shortstop that was booted by Marcus Semien. Bassitt then was replaced by lefty Danny Coulombe, who was added to the roster as the 26th man for the second game. He immediately allowed a single to Narvaez to load the bases.
Engel then followed with a two-run single to center to make it 5-2.
"There were a couple of pitches I wish I had back, but I felt really good," Bassitt said.
The A's rallied in the eighth. Dustin Fowler and Semien led off with back-to-back singles to chase Giolito. Lefty Jace Fry came on and walked pinch-hitter Stephen Piscotty to load the bases. Davis then singled off righty Chris Volstad to score two and trim the deficit to 5-4.
With runners on first and third and no outs, the A's had a prime opportunity for a big inning. But Olson lined out to short, Mark Canha struck out and Chad Pinder grounded into a forceout.
"We had 'em on the ropes," Melvin said. "[Olson] hits that ball as hard as you can hit it right at the shortstop. Then we get a strikeout and another hard-hit ball to short, but we just came up one at-bat short from at least tying the game."
Anderson's leadoff homer in the bottom of the eighth provided an insurance run.
SOUND SMART According to Statcast™, Olson's homer to right had an exit velocity of 113.3 mph, the fastest by an A's player since tracking began in 2015. Davis had the previous mark of 113.2, in 2016.
HE SAID IT "We'll never know. It was hit hard enough for it. Not really sure." -- Melvin, on whether a double play could have been turned on Semien's sixth-inning error
UP NEXT The A's and White Sox play a matinee on Saturday with a first pitch of 11:10 a.m. PT. Daniel Mengden takes the mound looking to rebound from his recent struggles. The right-hander is 0-2 with a 10.05 ERA in three June starts. He has allowed at least two home runs in each of his last three starts and his eight homers allowed in June are tied for the most in the Majors. Dylan Covey pitches for the White Sox.
John Jackson is a contributor to MLB.com based in Chicago.