MINNEAPOLIS — The way their offense has been going lately, the Yankees can ill afford many mistake pitches or fielding miscues.

They piled up a few too many on Tuesday night and that led to their first three-game losing streak of the season.

The Yankees struck first, but it didn’t ultimately matter, as their small margin for error proved costly in what turned into a 6-2 loss to the Twins at Target Field.

With the win, the Twins (14-10) clinched their first season-series victory over the Yankees (13-11) since 2001. Long tormented by the Yankees, the Twins have won four of the first six games between the teams this season ahead of the series finale Wednesday afternoon.

The Yankees have scored three runs or fewer runs in seven of their last eight games.

“Obviously we’ve done a lot of [scoring] one and two runs. That doesn’t lend itself to much margin for error on the mound,” manager Aaron Boone said. “We’ve got to change it. We gotta hopefully build a little bit on today in the fact that this was better than [Monday]. But we gotta hang some crooked numbers up there, bottom line.”

The score Tuesday night was tied 2-2 heading into the sixth inning, when the Twins jumped on top for good against Nestor Cortes and Ron Marinaccio.

Jorge Polanco led off against Cortes with a deep fly ball to left-center field.

Left fielder Aaron Hicks made a long run to give himself a chance for a catch, but still couldn’t come up with it, just in front of the wall.

Byron Buxton came up next and worked a full count before he got a 3-2 cutter over the plate and crushing it for a two-run home run. That gave the Twins a 4-2 lead and knocked Cortes out of the game.

“I felt like I could have done a better job locating the inside part of the plate in that last inning,” Cortes said. “Byron Buxton hit a cutter that didn’t get in enough. I think that was the difference in the game right there.”

Marinaccio entered from the bullpen and allowed an infield single around a pair of strikeouts.

But his first pitch to Trevor Larnach was a changeup that caught too much of the plate and was clobbered for another two-run homer to right-center field.

The Yankees’ lineup, meanwhile, lacked that kind of thump against Twins right-hander Joe Ryan.

They scattered five singles over the first two innings, but that only led to one run. Ryan went on to mostly cruise across seven strong innings, striking out seven and walking none.

Ryan, Jorge Lopez and Jhoan Duran retired 13 of the final 14 batters they faced to end the game.

“[Monday] night we were, I felt like, dominated in a lot of ways,” Boone said. “Tonight, I felt like was different. You could sense that right from jump street as we were able to hit some balls on the screws to start. … But still not breaking through with that big one, that gapper that scores a couple or hit one in the seats.”

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A night after Aaron Judge said the Yankees had to be more aggressive early in games, he hit the first pitch he faced in the first inning for a single, took second on a wild pitch and scored on DJ LeMahieu’s opposite-field single for a 1-0 lead.

But Anthony Volpe’s third error in as many games opened the door for the Twins to take the lead in the third inning.

The speedy Michael A. Taylor led off with a squibber to the left of second base. Volpe reached down for it, but missed.

“It had weird spin, but still, it was hit soft enough that I gotta stay down on it and make the play,” said Volpe, who went 2-for-4 at the plate.

A pair of doubles from Donovan Solano and Polanco gave the Twins a 2-1 lead.

The Yankees tied it back up in the fifth when the Twins flubbed a potential inning-ending double play.

But from there, the bats went quiet again.

“Up and down, I thought better intent, better aggressiveness with the at-bats,” Boone said. “Now we gotta finish through and get some guys rolling.”