Cleveland's 20 wins this month mark its best total in almost 20 years.
With one more, the Indians will host the wild-card game.
With at least a share of the AL wild card already assured, the visiting Indians seek a 10th straight win in Sunday's season finale against the Minnesota Twins.
"We want to keep this roll going," Nick Swisher said after Saturday's 5-1 win. "This is so much fun."
If Cleveland (91-70) loses and Tampa Bay and Texas both win Sunday, the ensuing three-way tie would result in a one-game playoff between Tampa Bay and Cleveland at Progressive Field on Monday. The winner would get one wild card with the loser playing a win-or-go-home contest at Texas on Tuesday.
A win Sunday, though, means the Indians host the wild-card game on Wednesday.
"For all we've been through, I'd love to play a game in Cleveland," manager Terry Francona told the team's official website. "I think that would be really rewarding for the fans."
Five of Cleveland's 20 wins in September - the franchise's most in a month since August 1995 - have come with Ubaldo Jimenez (12-9, 3.38 ERA) on the mound.
Boasting a 1.76 ERA since July 28, the right-hander has been even better in September, going 3-0 with a 1.04 ERA in five starts. He couldn't pick up the win Tuesday, despite holding the Chicago White Sox to two runs in 6 1-3 innings of Cleveland's 5-4 comeback victory. He struck out seven, and is averaging 11.14 strikeouts per nine innings over his last eight starts.
Jimenez has generally fared well against the Twins, posting a 3.21 ERA in five starts. He held them to two runs in six innings of a 5-1 loss on Aug. 23.
The Twins turn to Scott Diamond (6-12, 5.54), who has allowed at least three runs in four straight starts and 17 of 23 this season. A trip to the minors hardly helped, as he is 1-2 with a 5.71 ERA in three starts since his return. Tuesday marked another hiccup for the left-hander, as he allowed four runs in 6 1-3 innings of a 4-2 loss to Detroit.
"Everything kind of just comes in clumps for me," Diamond said. "That's just the way it's been this season. I've been consistently bad for one inning."
A three-run fifth knocked Diamond out of 7-1 loss to Cleveland on July 21, when he allowed six runs in 4 2-3 innings.
His 3.53 strikeouts per nine innings are the lowest of any pitcher with at least 125 innings thrown. He has eight over 41 2-3 innings in his last eight starts.
With a loss, Minnesota (66-95) would have at least 96 defeats in three straight years for the first time in franchise history.
"I had more than one of them come up and apologize to me," manager Ron Gardenhire said. "I don't need that. I know what they're giving me. They're giving me a lot. I appreciate the efforts and they don't have to apologize for anything."
Cleveland's Carlos Santana has two home runs and five doubles over a six-game hitting streak.
Jason Kipnis is 11 for 24 (.458) over a six-game streak of his own. He is also batting .423 with 24 RBIs in 18 games against Minnesota this season.