CLEVELAND -- For roughly eight hours on Saturday, the competitive portion of the Twins’ season appeared to be functionally over, a doubleheader sweep at the hands of the division-leading Guardians looming as an inevitability inching ever closer.

The Twins found a way to dig deep. Really, really deep.

They found a miracle rally against the Cleveland bullpen, with Nick Gordon’s game-tying two-run homer off James Karinchak capping a five-run eighth inning. As the game between two fatigued teams playing a split doubleheader dragged ever deeper into extra innings, depleted reliever after depleted reliever delivered escape after escape as the Twins emptied their bench and used every available arm they could muster for a grueling 15 innings.

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It still wasn’t enough. The Twins’ playoff hopes still mathematically exist, but their fate appears all but secure after a 5-1 defeat in the first game of the doubleheader was followed by a 7-6 heartbreaker of a loss finally sealed when Amed Rosario’s ground ball hit off the end of the glove of backup shortstop Jermaine Palacios in the 15th inning -- five hours and 24 minutes after the nightcap began.

“It’s hard to swallow being at this point in the season and being this far out,” Twins manager Rocco Baldelli said. “I know we’re going to go out there and continue to fight in every possible way from today until the last regular season game, and then we’ll see what happens.”

For as proud as Baldelli and the Twins were of their resolve on Saturday, the hard reality of the numbers now speak louder than anything: The Twins are seven games back in the division with 17 to go, with only two remaining head-to-head matchups against Cleveland.

They entered this series with a four-game deficit and five to play against the division-leading Guardians, still in control of their destiny. With losses in the first three, the best they can do is to leave Cleveland on Monday trailing by five. They’ve lost eight in a row to Cleveland, one shy of the longest such streak in club history.

“It's tough,” Carlos Correa said. “We started Spring Training with a goal of winning the division, and [with] 17 games left, it's a little tougher.”

It wouldn’t be fair to compare this war of attrition to a 12-round fight, because it went even deeper into reaches hitherto unknown, becoming the longest Twins game by both innings and time in the automatic runner era, surpassing the previous marks of 12 innings and five hours, 14 minutes.

And hard as the Twins fought through a last stand that featured not only the five-run comeback in the eighth, but also a game-saving assist at home by outfielder Mark Contreras and even a too-lucky-to-be-true play in the 15th in which a grounder bounced to third baseman Gio Urshela in the perfect spot for him to tag the lead runner, it still ended in a trying defeat -- and that’s been the common thread in these matchups that have sunk the Twins this season.

The Twins are now 5-12 against the Guardians, and all too many of those losses have been tantalizingly within reach and emblematic of the overall issues that ultimately sank them. The last time Minnesota visited Cleveland, the Twins’ bullpen blew three leads in the eighth inning or later, and recent losses on Friday and in Saturday’s nightcap made it eight defeats in which the Guardians scored the winning run in the seventh inning or later.

And when the bullpen shone as it did on Saturday, the Twins went 2-for-19 with runners in scoring position in extras, including a streak of 13 straight hitless at-bats from the eighth to the 12th -- another season-long issue.

Less than two weeks ago, on Sept. 4, the Twins held a share of first place, and spoke with hope about their ability to take control with all these games against Cleveland. Now, they’re a depleted bunch with 18 players on the injured list, having suffered yet another futile ending after their most physically and emotionally draining effort of all, seemingly aware of the fact that the battle has almost drawn to its end.

“We're walking out of here feeling a lot of different emotions that you don't feel every day when you show up to the baseball field, and it's going to be impossible to describe all of them and lay them all out perfectly,” Baldelli said. “But I think there were even some tears shed with the emotion that goes into playing the game that way.”