Fister (9-13) lasted eight innings, allowing one run on three hits. He struck out five, did not issue a walk and won his fifth straight decision.
Don Kelly went 2-for-4 with a home run and two RBI for the Tigers, who claimed their first division crown since winning the AL East in 1987. They advanced to the playoffs for the 13th time in club history and the first time since 2006.
"This is only the first leg. It's not like we won the World Series. ... We're going to continue to play. Anyone that is a member of postseason competition can win it," Tigers manager Jim Leyland said.
Detroit is three games back of the AL East-leading New York Yankees for the best record in the league.
Trevor Cahill (11-14) surrendered three runs on nine hits over 6 2/3 frames to suffer the loss for Oakland, which won the opener of this series on Thursday.
Rick Porcello takes the hill this afternoon for the Tigers in search of his fourth straight winning decision. Porcello won his second straight start on Monday in Chicago, as he held the White Sox to three runs and six hits in 6 2/3 innings to improve to 14-8, while lowering his earned run average to 4.83.
Porcello beat the A's the last time he faced them, but is only 2-3 in six starts against Oakland with a 4.50 ERA.
Oakland will hand the ball today to lefty Gio Gonzalez, who is 13-12, with a 3.41 ERA. Gonzalez won for the fourth time in five starts on Monday against the LA Angels, as he allowed two runs and seven hits in 6 2/3 innings. He also struck out six and walked a batter.
Gonzalez has had his troubles with the Tigers and is 0-3 in four starts against them with a 6.87 ERA.
The A's have split their eight matchups with the Tigers this season.