Minnesota took their post-season place with a typically gritty performance, rallying for four runs in the bottom of the eighth to overcome a 4-2 deficit against the visiting Indians.
Slugger Jim Thome, who had earlier hit his 25th home run of the season and 589th of his career, started the late rally with a single, while Delmon Young and Orlando Hudson had RBI-doubles sandwiched around a run-scoring single from Denard Span.
Reliever Glen Perkins (1-1) got the win and Matt Capps posted his 15th save for Minnesota.
The victory was manager Ron Gardenhire's 800th in his career.
Despite a quick turnaround for a Wednesday afternoon game, the Twins remained in the clubhouse to see if they would finish the night as division champions.
"These guys aren't going to let me go home out there," Gardenhire told reporters. "I had a posse in here telling me 'we're staying'."
It was worth the wait as Oakland held off a bases-loaded threat in the top of the ninth before finishing off Chicago.
"It's just the first stepping stone, the milestone we've been trying to reach," second baseman Hudson said. "We still have a lot of baseball left."
Gardenhire has steered a consistent run of Twins success since 2002 but has yet to match the triumphs of predecessor and mentor Tom Kelly, who led Minnesota to World Series crowns in 1987 and 1991.
Despite a payroll less than half of the $200-plus million spent by the Yankees, Gardenhire has the Twins chasing New York (92-59) for the best record in the American League and the home field advantage it brings in the playoffs.
The Yankees increased their lead to 2 games over the Tampa Bay in the AL East with an 8-3 win over the Rays in New York.
(Reporting by Larry Fine, Editing by Greg Stutchbury and john O'Brien)