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 secured 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.
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 four-game series on Thursday.
DeJesus ended Fister's run with a two-out single in the seventh, but the Tigers had grabbed a 2-1 lead by then.
Kelly singled home Ramon Santiago, who began the third with a leadoff triple, to tie the game.
Betemit's sixth-inning, go-ahead triple followed Jhonny Peralta's single up the middle and Kelly's one-out blast to right capped the scoring in the seventh.
Following Crisp's leadoff double, Valverde retired the next three A's in succession, sealing the Tigers' 13th win in their last 14 games.
They head to the postseason trying to win the World Series for the first time since 1984, when they beat San Diego in five contests.
"Their late-inning bullpen guys are very good and they have good starting pitching across the board. They're a deep team," Athletics manager Bob Melvin said of the Tigers.
Fister made his ninth start of the season for the Tigers since being acquired in a six-player deal with the Mariners on July 30...In 2006, Detroit won the AL pennant as a wild card and lost the World Series in five games to St. Louis.