Kottaras' first triple of the season capped a four-run rally in the sixth inning and put the A's up 6-3. Oakland put the game away with a six-run ninth inning that Kottaras started with a single and Seth Smith highlighted with a three-run double.
The bottom of the Oakland lineup -- Smith, Josh Donaldson, Kottaras and Cliff Pennington -- was a combined 10-for-17 with eight RBI and seven runs scored.
Pat Neshek (2-1), who stopped a Detroit rally with a one-out appearance in the fifth, got the win. Anibal Sanchez (8-13) was charged with the first six Oakland runs and took the loss.
The Tigers scored twice in the second inning, with Gerald Laird and Austin Jackson getting the RBI, but the A's answered with single runs in the third and fifth as Donaldson scored the first run and Smith hit a home run for the other.
Detroit took a 3-2 lead in the bottom of the fifth with Prince Fielder RBI double but that edge wilted under Kottaras' triple. The Tigers made it 6-4 on an Andy Dirks home run but Oakland sent 10 batters to the plate in scoring six times in the ninth.