Verlander (1-0) yielded one run on three hits while walking four, becoming the first pitcher with 11 or more strikeouts in seven or fewer innings in an AL post-season game since 1999.
The Tigers' ace placed 79 of his 121 pitches for strikes and fanned five straight Athletics batters at one point as the Tigers took a 1-0 lead in the best-of-five series.
Alex Avila added a solo homer for Detroit.
Oakland's Jarrod Parker (0-1) was tagged with the loss, allowing three runs (two earned) on seven hits through 6 1/3 frames.
The right-hander mishandled Quintin Berry's infield grounder in the third inning, allowing Omar Infante to score for a 2-1 Detroit lead.
Coco Crisp provided Oakland's only offense by socking a solo homer to lead off the game.