MILWAUKEE — Cam Schlittler threw six shutout innings Saturday night, then gave way to a slow-motion train wreck at American Family Field.

The Yankees lineup had wasted opportunities to blow the game open throughout the night, then saw it all come back to bite them late as a leaky bullpen could not hold a two-run lead and ultimately fell to the Brewers in brutal fashion, 4-3 in 10 innings.

The Brewers (21-16) walked it off against Tim Hill, as William Contreras — who had tied the game in the bottom of the eighth with an RBI single off Camilo Doval — delivered a bases-loaded sacrifice fly to win it.

That situation was preceded by an unwise decision from Hill. The lefty ground-ball specialist had entered a tie game with runners on first and second and one out to face the left-handed-hitting Brice Turang. Hill got Turang to hit a chopper off the mound, but with no shot of a double play, Hill should have just gone to first base for the easy second out. Instead, he forced a long throw to try to get the lead runner at third, only to hit him and get no outs at all.

“I made a good pitch and then a bad decision afterwards,” Hill said. “Feel like my instincts told me third and my instincts were wrong.”

Hill has been the Yankees’ most reliable reliever all season and typically fields his position well, but did not with the game on the line Saturday.

“Obviously one out there, want to get the out, any out we can get,” manager Aaron Boone said. “So I just think his aggressive nature took over.”

If Hill had gotten the out at first, he could have intentionally walked the righty Contreras to face the left-handed-hitting Jake Bauers — who homered off Brent Headrick in the seventh to pull the Brewers within 2-1 — with the bases loaded and two outs.

Instead, Contreras won it and handed the Yankees (26-14) their third loss in their past four games — just a few days removed from winning 15 of 17 — and their first series loss since April 10-12, when they swept by the Rays. They will now try to avoid another sweep Sunday, when Carlos Rodón makes his season debut.

On a night when the Yankees went 3-for-14 with runners in scoring position, Ryan McMahon collected one of those hits in the top of the 10th when he came through with a two-out, two-strike single up the middle for the 3-2 lead. But Fernando Cruz quickly gave it up in the bottom half.

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He issued a leadoff walk to Luis Rengifo, who was trying to lay down a sacrifice bunt, and in the process spiked a fastball to the backstop, allowing the automatic runner to take third.

Ex-Yankee Gary Sanchez came up next and lofted a fly ball to right-center field that the Brewers decided was too shallow to test Aaron Judge’s arm. But they got the tying run in on the next at-bat, as Jackson Chourio poked a slow grounder to José Caballero’s right that the shortstop had no play on, at which point Boone called on Hill.

After a dominant Schlittler left the game with a 2-0 lead, Headrick immediately gave up his first home run of the year in the seventh before Doval allowed another run in the eighth.

David Bednar tossed a 12-pitch bottom of the ninth, and Boone said he considered sending him back out for the 10th, but ultimately decided not to after the closer had thrown a five-out save Tuesday.

“You don’t want to get in the habit of doing that over and over and felt really good about being lined up there with Cruz and Hill to get us through in the end,” Boone said. “So I did consider it a little bit, but once you realize if he’s going to finish that game, it might get up into that 30-35 [pitch range], and I just didn’t want to be in a position to do that with a full bullpen still behind him.”

The bigger issue was the Yankees not being able to cash in earlier in the game, stranding nine runners and giving their pitchers no margin for error. They put runners on first and second with no outs in the second inning and could not score; loaded the bases with no outs in the fourth and only scored once; and then put runners on first and second with no outs in the eighth and could not score again.

Paul Goldschmidt provided the 2-0 lead with a leadoff home run and an RBI single in the fourth inning, but that was all the Yankees got until the 10th.

“Obviously not being able to really break through is the difference there,” Boone said. “We had a chance to break it open, didn’t get that big hit enough tonight.”