After battling through 8 1/2 scoreless innings, the Athletics mounted a threat against Tigers reliever Al Alburquerque (0-1) when Yoenis Cespedes began the inning with single to right and went to third base on Seth Smith's base hit down the right field line.
Josh Riddick was intentionally walked to load the bases and Rick Porcello, making his first relief appearance of the year, was brought in to face Vogt.
But the Oakland catcher scorched a hit to left through a drawn-in infield for the game-winner, which evened the best-of-five ALDS at 1-1.
Grant Balfour (1-0) earned the decision after A's rookie Sonny Gray had blanked the Tigers on four hits over eight innings, walking two and striking out nine.
Detroit starter Justin Verlander tossed seven innings of shutout ball, scattering four hits while walking one and fanning 11.
The Tigers have failed to score a run over 17 straight innings in the ALDS.