CHICAGO — The Yankees’ mess of a bullpen blew another one Tuesday night.

And this might have been the worst of all.

After a stirring eighth-inning rally gave the Yankees a two-run lead, they could not close it out. The White Sox defeated the Yankees, 4-3, on a walk-off two-out, two-run single by Jose Abreu off Dellin Betances at Guaranteed Rate Field.

Betances, who brought a 1.09 ERA into the night but whom Joe Girardi wanted to stay away from as he’d worked back-to-back games, walked Tim Anderson with one out in the ninth. Willy Garcia pinch ran. Betances fell behind Alen Hanson 3-and-0, eventually walking him. Betances hit Yolmer Sanchez to load the bases but he got Melky Cabrera to foul out. After falling behind Jose Abreu 2-and-0, the dangerous first baseman sent a 2-and-1 breaking ball to left to win it.

“I can’t just give free bases there,” Betances said. “My offspeed, I couldn’t get it over for strikes. I couldn’t make pitches when I needed to.”

Girardi said he was without Aroldis Chapman Tuesday because he, like Betances, had worked back-to-back games. He said he might have been tempted to use the closer if he had not just come off the DL. Girardi was also without Chad Green.

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And so, after Aaron Judge and Gary Sanchez came through with huge eighth-inning hits that turned a 1-0 deficit into a 3-1 lead for the Yankees (41-34), Girardi’s choice in the bottom half was rookie righthander Domingo German and after consecutive walks to start the inning, slumping righty Tyler Clippard.

“The bullpen’s been used a lot,” Girardi said. “It’s just we’ve kind of been out of sorts because of some injuries and some struggles, and maybe if you get Clip [Clippard] going again and you get Adam [Warren] back sometime next week, everything kind of settles in.”

But they’re not there yet and Tuesday night the Yankees suffered their 14th blown save in their first 75 games. According to researcher Katie Sharp, the Yankees had five blown saves through the first 75 games last season.

It was a crazy evening, most of the craziness bunched into the final two innings.

The eighth-inning hits, a two-out game-tying RBI single by Judge and a two-run double by Sanchez, looked as if they’d keep Luis Severino from taking what would have been a brutal loss.

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The 23-year-old righthander was terrific against the White Sox (33-43), striking out a career-high 12 over seven innings in which he allowed one run, six hits and zero walks.

White Sox lefthander Jose Quintana, a possible trade target for the Yankees — the case the last couple of seasons — was a tad better. Quintana, a former Yankees farmhand, allowed two hits over 6 1⁄3 scoreless innings in which he walked four and struck out six.

Severino, who had allowed a combined nine runs over his previous two outs, lowered his ERA from 3.30 to 3.15.

“Everything was working,” said Severino, whose fastball and slider were the sharpest they’ve been.

After the brilliance of Severino and the hits by Judge and Sanchez, the Bombers still had to record six more outs, which turned out to be too much to ask.

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After the back-to-back walks issued by German, Clippard, who coming in had allowed 11 runs over his previous seven outings, immediately fired a wild pitch, advancing the runners. He then walked Melky Cabrera on four pitches, loading the bases for Abreu.

Clippard got ahead of Abreu, with 13 homers coming in, 0-and-2, and struck him out. Clippard got Avisail Garcia to pop to short right for the second out, but couldn’t quite finish things off, walking Todd Frazier to force in a run to make it 3-2. He did strike out rookie Matt Davidson to keep it there.

“Felt like myself tonight,” Clippard said. “Huge step in the right direction.”

Perhaps for him but not yet for the club overall.

“That’s a hard loss,” Girardi said. “But we’ll bounce back tomorrow.”