CLEVELAND >> The Twins’ realistic chances of repeating as American League Central champions vanished weeks ago. On Thursday, it became official.

The Twins were mathematically eliminated from winning the division with a 3-2, 10-inning loss to the Cleveland Guardians on Thursday afternoon at Progressive Field. Their only hopes of making it to the postseason rest on qualifying as a wild card, and with their latest loss, they are now tied with the Detroit Tigers for the final playoff spot.

The Twins (80-73) lost three of their four games in Cleveland, and all the losses were late heartbreakers, with the final two coming on walk-off hits in extra innings.“I think we can easily sit here, very easily can sit here and we could have won all four of those games,” catcher Ryan Jeffers said. “At the end of the day, they showed why they’re the better team. Why they’ve been better this year is they’re able to finish those games out, the games that we haven’t been able to.”

After being walked off on Wednesday night, Twins relievers bent but did not break during the middle of Thursday’s game, stranding two runners for three straight innings from the fifth through the seventh. Louie Varland and Griffin Jax then got through the eighth and ninth innings quickly to help send the game to extras.

But the Guardians (89-65) broke through in the 10th, walking off the Twins on an Andrés Giménez single off Caleb Thielbar that brought home automatic runner José Ramírez and punched their ticket to the postseason.

It came after the Twins were unable to do anything with their opportunity in the top of the inning in which they loaded the bases with just one out for stars Carlos Correa and Byron Buxton, who were unable to convert those runners into runs. Correa fouled out to first and Buxton lined out to right field.

“It’s a great opportunity to win the game. I want to be in that spot,” manager Rocco Baldelli said. “What else do we want in the 10th inning than to have those guys at the plate with the bases loaded? … That’s where we want to be. When we have those opportunities, we have to come through.”

The Twins were outhit 11-3, and Guardians pitchers retired 14 batters in order from the fifth through the ninth innings. The Twins scored their only runs in the fifth after Kyle Farmer led off with a double, Willi Castro later walked, and both came home to score on the same play: a Manuel Margot single that was bobbled by center fielder Lane Thomas.

Margot’s hit gave the Twins the lead, but it was their last hit of the day.

“By a lot of measures, they have the best bullpen this year in the history of baseball,” Baldelli said. “It doesn’t mean we can’t go out there and drive some runs in and win a game.”

Twins starting pitcher Simeon Woods Richardson surrendered a solo home run to designated hitter Kyle Manzardo in the first inning but maneuvered through 4? innings and did not allow another run, making way for newly acquired pitcher Cole Irvin in the fifth.

The Guardians tied it off Irvin in the sixth on a Brayan Rocchio sacrifice fly after the Guardians had loaded the bases on a single just past the reach of second baseman Kyle Farmer, an infield hit to Castro at short and a bloop single.

And after that, their bullpen stifled the Twins, who now must beat out the Tigers, whom they hold the tiebreaker over, in a nine-game sprint to October.

“We’re just trying to restart and go from there,” outfielder Matt Wallner said. “If you’re looking at it from the outside, the odds probably aren’t in our favor just with how they’ve been going and how we’ve been going, so something’s got to change.”