The teams held identical 61-87 records and sat 20 1/2 games out of first place in the American League Central prior to Minnesota's 6-4 victory on Wednesday. Catching the Royals for third place in the division is unlikely, but not out of reach.
Minnesota manager Ron Gardenhire is simply looking for his team to improve as much as possible before the season's end.
"The standings have been long gone," he said. "Sure, you want to move up -- that's all good and fun. But I really just want to come out and play better baseball. ... It's not about helping some other team, it's about showing respect to the game and playing our game."
One Twins starter who could sorely use some improvement is Esmerling Vasquez, who will get the ball in the teams' series finale with Cleveland on Thursday. He is 0-2 with a 7.53 ERA in three starts this season.
Similarly, while the Indians' rough month of August put them out of contention -- they went 5-24 -- the club is still using the end of the season as a gauge of its players' mettle.
"It's time to evaluate and see character," manager Manny Acta said. "We've seen how people's character was tested throughout the whole ordeal of the second half. That's something that's being evaluated. Who can handle it? Who can't? Who's going to point fingers?"
Thursday starter Corey Kluber handled the Twins well once and not so well another time in his two outings against Minnesota this season. He held the Twins to one earned run on six hits in six innings on Aug. 7 before giving up four earned runs on eight hits in just 3 2/3 innings on Sept. 9.
Twins: Mastroianni available only to pinch-run
Darin Mastroianni scored the go-ahead run in Minnesota's win over Cleveland on Tuesday, but jammed his finger on a bat lying beside the plate while sliding headfirst into home. He injured the tendon in his left middle finger and is now only available for use as a pinch-runner for the remainder of the season.
"Him diving in headfirst into home plate with a bat there, he probably didn't see the bat," Gardenhire said. "It's a scary place to dive into anyway, and it ended up costing him a little bit here. But it was a very good baserunning play, other than the finger part."
Chris Herrmann made the first start of his Major League career on Wednesday, catching Liam Hendriks and also driving in the first run of his career. Herrmann grounded into a fielder's choice in the fifth inning to score Justin Morneau from third.
"He can hit," Gardenhire said. "I've seen him in Spring Training. I don't worry about him."
Indians: Hafner returns from DL
Designated hitter Travis Hafner went 0-for-3 on Wednesday, playing his first game since Aug. 5, when a back injury sent him to the disabled list.
Hafner is hitting .235 with 11 home runs and 32 RBIs in 61 games this season.
"We're a better team when Hafner is in the lineup," Acta said. "Hafner has been here for a long time, and if he's ready to play, he deserves to play. Plus, he's not going to be taking any at-bats away from the guys that we really need to see."
Hafner will be limited to playing three times per week through the end of the season, at the advice of Cleveland's medical staff. He will not start on Thursday.
Cleveland will likely decide soon whether Roberto Hernandez will pitch again before the end of the season. Hernandez -- who has been out with an ankle injury since Aug. 27 -- was fine during a bullpen session on Tuesday but experienced limited mobility during other drills. He is scheduled to throw off the mound and participate in another workout on Friday.
Morneau needs one more RBI against Cleveland -- his 21st of the season -- to claim the title for most runs driven in by a Twin against the Indians in a single season. Morneau is currently tied with Harmon Killebrew, who recorded 20 RBIs against the Indians in 1962.
With Wednesday's victory, Minnesota tied its single-season win total against the Indians. A win on Thursday would set a new mark for the Twins, who also collected 12 wins over the Indians in 2010, '04 and 1962.