The first two Yankees pitchers to give up runs Tuesday had been trending poorly for an extended stretch.

The third, Brent Headrick, had not.

But after the Yankees had fought back to take three separate leads, Headrick picked a poor time for a rare bad outing, giving up three runs in the eighth inning to sink his team in a back-and-forth 9-7 loss to the Astros in The Bronx.

On a night when Will Warren and then Fernando Cruz got hit around and failed to preserve leads, Yankees hitters picked them up in a rare role reversal, which is how Headrick had a 6-5 lead to protect entering the top of the eighth.

But the lefty could not do what he has most of the season and throw up a zero, instead squandering the lead as the Yankees (74-57) wasted a chance to pick up another game on the Rays, who remained 3 ¹/₂ games up for the division lead.

The Red Sox, who will arrive in town this weekend for a huge four-game showdown, won in extra innings and moved within 1 ¹/₂ games of the Yankees for the top AL wild card.

The Astros (66-66), who used their off day Monday to fire general manager Dana Brown with five weeks left in the regular season, are still right in the thick of the playoff race (thanks to a weak American League and in particular AL West) and played like a desperate bunch.

They scored in six of the nine innings, erasing Yankees leads of 3-2, 5-3 and 6-5.

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“They beat our guys tonight, so you got to give them some credit,” manager Aaron Boone said. “We kept answering for the most part, too, but they just did a little bit more offensively tonight.”

Headrick, whom Boone said he was reluctant to use Tuesday because of his rising workload (his 68 appearances are the second-most in the majors), had given up a total of three runs over his past 21 games before Tuesday.

But Yainer Diaz took him deep for his second home run of the night — only the fourth home run Headrick has allowed this season — to tie it 6-6 with one out.

The Astros then took the 8-6 lead by stringing together a Jeremy Peña single, Yordan Alvarez triple and Isaac Paredes single off Headrick.

“I went in feeling good,” Headrick said. “I thought I made some good pitches at times and sometimes baseball just happens. Best thing I can do is flush it and come out tomorrow.”

The Yankees threatened to come back once more in the bottom of the eighth, but their rally ended at just one run.

Another encouraging night for their offense was negated by their pitchers giving up more than five runs for the first time since Aug. 3.

Luis García Jr. did almost everything he could for the Yankees on a four-hit night, twice giving them the lead — his two-run blast making it 5-3 in the fifth inning and an RBI double putting them back on top 6-5 in the seventh.

But neither one lasted. The first was because of Cruz, who continued to struggle in one of the more concerning trends for the bullpen of late.

The righty, who entered in relief of Warren (five innings, three runs) walked a batter in the sixth and then with two outs, left a 91.5 mph fastball down the middle for Peña, who drilled a two-run shot that tied the game 5-5.

Cruz has now given up at least one run in eight of his past 16 appearances, posting a 5.93 ERA in 13 ²/₃ innings during that stretch.

Of the seven home runs he has allowed this season, four have come in 10 August games.

“It’s just that part of the year that, this is a marathon, there’s ups and downs like every player has,” said Cruz, who met with a trainer before speaking with reporters but insisted he was “feeling good” after his 61st appearance of the year. “Every player has their battles with their bodies and stuff, but we’re going to be great.”

In his second game back from the IL, Cody Bellinger had gotten the Yankees lineup started, taking Astros rookie starter Ethan Pecko deep for a three-run homer — his first since June 17 — that put them ahead 3-2 in the third inning.

But like all three of their leads Tuesday, it did not last long.