Bonderman (8-9) turned in perhaps his best start of the season. He matched a season high in innings pitched and struck out eight, while allowing just one run on three hits and a walk.
"Obviously they're a great team, they're in the position to make the playoffs," Bonderman said. "We're just trying to go out and play good baseball day in and day out. Doesn't matter who you play."
Avila's double came in a four-run fourth inning, during which Brandon Inge hit a two-run single. Ryan Raburn added two hits and scored twice for the Tigers, who have won the last two games in the set after dropping Monday's opener.
John Danks (13-10) took the loss after allowing five runs -- two earned -- in six innings. He gave up eight hits and walked three.
"We feel like we still have a chance," Danks said. "We're kind of shooting ourselves in the foot a little bit. The last couple nights we haven't been playing very well."
Following today's finale Chicago will start a nine-game homestand that will include a visit from the Twins.
Getting the call for the White Sox this afternoon will be right-hander Gavin Floyd, who has been terrific in his last three starts (2-1). Floyd earned a win on Saturday in Boston, holding the Red Sox to a runs and five hits in six innings to run his record to 10-11, while lowering his earned run average to 3.78.
Floyd, who has allowed just five runs in his last three starts spanning 19 2/3 innings, has been terrific in his career against the Tigers, posting a perfect 5-0 record to go along with a 3.20 ERA in 13 starts.
Detroit, meanwhile, will counter with Rick Porcello, who has won his last three starts and is 8-11 on the season with a 5.20 ERA. Porcello's latest win came on Saturday in Kansas City, as he limited the Royals to four runs and seven hits in seven innings.
While Floyd has had success against the Tigers, Porcello has had nothing but bad luck against his opponent, going 0-4 in five starts against Detroit with an 8.67 ERA.
Chicago is 5-3 in Detroit this season.