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The Twins and Cleveland battled like the American League Central was on the line.

Because it was.

Sure, it's only June, and there are close to 100 games left to play before the postseason picture comes into focus. But after the Twins led the division for a solid month — and most of that time with a multiple-game lead — they've now made room for the Guardians at the top.

After an 11-inning grind, Cleveland won 6-5 at Target Field in front of an announced crowd of 22,341 on Tuesday.

Jose Miranda's bid for a two-out, two-run, game-winning home run in the bottom of the 11th fell a few feet short of the left field fence as the Guardians won for the 16th time in 20 games to catch the first-place Twins (35-28). Cleveland is 38-31 with two games left in this series before the teams meet five times in four days in Cleveland starting Monday.

Luis Arraez belted a three-run home run to give the Twins a 5-3 lead in the seventh inning, but Twins reliever Emilio Pagan couldn't hold the lead. He gave up a two-run shot to Franmil Reyes in the top of the eighth that tied the score.

Neither team scored in the 10th, although the Twins had two on and no outs before Carlos Correa, Max Kepler and Gary Sanchez struck out.

Andres Gimenez broke the deadlock in the top of the 11th inning, delivering an RBI single with Griffin Jax on the mound. Miranda's long fly in the bottom of the inning off Cleveland closer Emmanuel Clase fell just short.

Twins starter Joe Ryan allowed three hits and a run from Oscar Gonzalez's RBI double in the first inning. He surrendered three more hits and two runs in the third, the latter off Josh Naylor's home run. Ryan managed to last six innings and 101 pitches, though, striking out the final three batters he faced.

Alex Kirilloff helped the Twins finally make an offensive impact, hitting a two-run double in the fourth off Cleveland starter Aaron Civale. Arraez's homer put the Twins in position to win before Reyes tied it after working Pagan to a full count.

"I made a mistake with it there 3-2, and he didn't miss it," Pagan said. "I don't think it was the wrong pitch. I just didn't execute it. I threw 17 pitches [Tuesday]. I threw 16 of them right where I wanted to. Life of the bullpen. You make a mistake with a man on and it changes the game completely."

Pagan admitted to watching the standings very closely since Opening Day, something he said he has done since his days as a fan. So he's very aware of how hot Cleveland had been playing and what it means now that the Guardians are also on top.

Ryan is the opposite, saying he doesn't like to look at any stats and prefers to make the majors feel like a "backfield game."

Twins manager Rocco Baldelli tried to keep the outcome of this one game in June within perspective.

"The standings in June don't really carry any significance for me," Baldelli said, "and those are things that we said when we were in first place. It doesn't matter what place you're in, as long as you've got a chance. We've got plenty of games to play. We've put ourselves in a good spot to go forward. We need to get ready for [Wednesday]. We need to get ready to go out there and beat these guys and outplay them."