Danks (1-2) struck out six and walked one as Chicago notched only their second win in 12 games.
The result also represented a form reversal for the Athletics, who came in with an 18-3 record in their previous 21 games.
Detroit’s Prince Fielder hit a bases-clearing double in the second inning to lay the foundation for the Tigers’ 6-4 win over the Cleveland Indians.
The American League Central-leading Tigers extended their division lead over the Indians to 4.5 games.
Detroit starter Rick Porcello (3-3) gave up one earned run while striking out seven over six innings.
Toronto’s Rajai Davis hit an RBI single in the 18th inning to give the Blue Jays a 4-3 win over the Texas Rangers in a game that matched the longest in club history for both teams.
New York starter Andy Pettitte allowed three hits over 7-1/3 innings to earn his 250th career victory, leading the Yankees to a 3-1 win over the Seattle Mariners.
San Diego’s Kyle Blanks hit a two-run homer off the foul screen which helped the Padres to a 4-2 win over the Colorado Rockies.
Pittsburgh’s A.J. Burnett pitched into the ninth inning go steer the Pirates to a 6-2 win over the Chicago Cubs.
Minnesota’s Ryan Doumit singled in the go-ahead run in the 11th inning as the Twins edged the Washington Nationals 4-3 in their interleague clash.
Milwaukee’s Jean Segura homered and Jonathan Lucroy hit a tiebreaking RBI double in the sixth inning, lifting the Brewers to a 4-3 win over the Philadelphia Phillies.
Kansas City’s Ervin Santana pitched seven snappy innings and finally got some run support as the Royals downed the Houston Astros 7-2.
Miami’s Adeiny Hechavarria hit an RBI single in the 20th inning as the Marlins outlasted the New York Mets 2-1 in the longest major league game for three years.