HOUSTON — The Houston Astros were running out of chances, energy, warm bodies and life late Saturday night, in their third game in three days, in their second city and second time zone in 24 hours, near the end of the third week of the postseason and deep into their seventh straight month of playing baseball together.

And somewhere deep down, they understood they were nearing last chances. Win or lose, there would be a tomorrow. But tomorrow’s tomorrow was no given.

But what they had, even at their most dire moment, was José Altuve. And what Altuve had was a bat. And what that bat had was one more mighty swing.

In the bottom of the ninth inning Saturday night, in Game 6 of the American League Championship Series, Altuve’s bat propelled a slider from Aroldis Chapman, the New York Yankees’ flamethrowing closer, over the wall in left — a two-run homer that ended the ALCS and put the Astros into the World Series against the Washington Nationals.

They will soon raise another AL pennant in Houston, the second in three years, after a dramatic 6-4 victory in Game 6 of the ALCS, which saw the Astros end the Yankees’ season for the third time in five years. The Astros are loaded with high-end talent and blessed with ample creativity and resolve — but after the high-wire act they pulled off with their pitching in Game 6, they were also in desperate need of a day off.

The Astros were two outs away from victory, and the Yankees two outs from oblivion, when DJ LeMahieu, the Yankees’ first baseman, smashed a two-run, opposite-field homer off Astros closer Roberto Osuna to tie the score — leaving the Astros players doubled over in anguish and the ecstatic Yankees on the top step of their dugout.

LeMahieu’s homer came at the end of a 10-pitch at-bat in which he fouled off four straight two-strike pitches from Osuna.

Having led the entire game, the Astros were suddenly in both an emotional hole and a personnel one. They had blown through all the best arms in their bullpen, while the Yankees still had their closer, Chapman, ready in theirs.

In lieu of fourth starters, both teams opted for the once-dreaded, now-trendy bullpen game Saturday night, started by New York’s Chad Green and Houston’s Brad Peacock.

It was still a jarring sight given the stakes. It was also, if we’re being honest, kind of fun.

On a 1-to-10 scale of organized chaos, where one is the running of the bulls in Pamplona and 10 is a 3-year-old’s birthday party at Chuck E. Cheese, a double-bullpen game on the second weekend of a League Championship Series is something like a six. Unofficial press box oddsmakers put the over-under on the time-of-game at four hours (it was 4:08), the over-under on pitching changes at 12.5 (there were 11).

By the bottom of the first, the Astros had a 3-0 lead, courtesy of Yuli Gurriel’s three-run homer off Green.

By the top of the second, the Yankees had brought the go-ahead run to the plate. By the bottom of the second, both teams were on their second pitchers of the night.

By the top of the third, the Yankees had put the go-ahead run on base, and the game was visited by its fifth pitcher of the night. And on and on it went.

To understand how two exceptional teams, winners of 210 regular season games and payroll-spenders of nearly $400 million between them, with Cy Young winners, multiyear all-stars and future Hall of Famers populating their pitching staffs, wound up with a pair of solid but unheralded relief pitchers starting for them in Game 6 of the ALCS, you must begin with the rise of the opener as a pitching strategy beginning with the Tampa Bay Rays in 2018 — and its subsequent spread across the game.

You must recall, as well, that both teams lost their presumptive No. 4 starters down the stretch — the Astros’ Wade Miley to acute underperformance and the Yankees’ Domingo German to a domestic violence suspension.

Then there were the immediate factors spawned by the events of the past few days: Wednesday night’s rainout in New York, which counted among its casualties Friday’s scheduled travel day; the Yankees’ victory in Game 5 on Friday night in the Bronx, which kept the series alive; and the desires of both teams to hold their aces, Cole and Luis Severino, in reserve for a potential Game 7.

And so, Game 6 began at 7:09 p.m. Houston time with Peacock, who had closed out Game 5 for the Astros, on the mound, thus making him the first pitcher since Firpo Marberry of the 1924 Washington Senators to start a playoff game the day after finishing one.

In a game such as this, the managers are bound to have a larger say in the outcome than is typical. New York’s Aaron Boone and Houston’s A.J. Hinch sequenced their pitching with a fluid combination of scripted preferences and on-the-fly reaction.

The Astros suffered a setback in the top of the third when Ryan Pressley, at his best a high-leverage monster with an unhittable curveball, suffered a knee injury while fielding a comebacker that stranded the bases loaded.

The Astros chose to go without a lefty on their staff for this series, owing to the overwhelming right-handedness of the Yankees’ lineup, and Jose Urquidy’s excellent change-up, which helped him hold lefties to a .530 on-base-plus-slugging percentage this season, was one reason. It was Urquidy who in the sixth inning was saved by Reddick’s diving catch in right on a liner by Brett Gardner, a left-handed hitter.

From there, Hinch could deploy his best arms in a more or less conventional manner — Will Harris for four outs, Joe Smith for three. In the ninth, he had Osuna, an elite closer, warmed and ready to go. But Yankees third baseman Gio Urshela greeted him with a sharp single, and two batters later, LeMahieu weeded through nine pitches until he found one, a 94-mph cutter, he could drive to right.

A hundred years ago, the Yankees reached the end of the 1910s without a World Series appearance. On Dec. 26, 1919, they purchased a spindly-legged pitcher-turned-outfielder named Babe Ruth for $100,000 from the Boston Red Sox, won three championships behind him in the 1920s and never again endured a decade without at least getting to the final series — until the decade that comes to a close later this month.

Over the course of a 103-win season, the Yankees rarely came up against a team that was better. But over six games in this ALCS, it became clear that they had — if only by the smallest of margins, a single Altuve.

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