Coke (1-2) limited the Athletics to three hits in seven innings, walking two and fanning two while allowing only one runner to get as far as third base.
Ryan Rayburn smacked an RBI double in the seventh inning off reliever Tyson Ross (1-1) to break up a scoreless pitcher's duel.
Ramon Santiago added two hits and drove in a run for the Tigers, who took the first of a four-game series in Oakland.
A's starter Gio Gonzalez tossed six shutout innings, yielding only two hits while walking six and striking out six in a no-decision.
Celebrity Families of 2014 [PHOTOS]