The game was in doubt until the final out, but the Boston Red Sox are moving on to the American League Championship Series. (Julie Jacobson/Associated Press)

The eyes went from the ball, soaring into the black sky and beginning its reentry to earth’s atmosphere, to the glove, raised above the left fielder’s head and approaching, approaching, approaching the left-field wall. The ears went from the roar of the Yankee Stadium crowd at the ball’s impact with Gary Sanchez’s bat, to the sad and brutal exhale of a season dying away in Andrew Benintendi’s glove. And the mind, it went straight to the crux of the matter:

What had just separated the Boston Red Sox’s imminent clinching of the American League Division Series from a crushing, devastating defeat to the rival New York Yankees in Game 4 — a win that was remarkably easy and clean until all of a sudden it wasn’t — was a capricious breath of wind, a couple of spherical rotations of a baseball, a gift from the fates.

Because Sanchez’s high drive to left off Red Sox closer Craig Kimbrel with one out in the bottom of the ninth inning Tuesday night landed in Benintendi’s glove at the warning track, and not over the wall for what would have been a game-winning, walk-off grand slam, the Red Sox managed to escape the Bronx with a harrowing 4-3 victory that clinched the series and sent them into the AL Championship Series against the Houston Astros, beginning Saturday night at Fenway Park.

The final out, on Kimbrel’s 28th pitch of the inning, came on a slow grounder to third by Gleyber Torres, which required a fine charging play from third baseman Eduardo Nunez, a long stretch by first baseman Steve Pearce and — finally — an awkward and anticlimactic replay review to confirm the out call at first base, as the Red Sox first celebrated, then waited, then celebrated again in a teeming, joyous huddle near the mound.

And so, four games between the Red Sox and Yankees in October, the first meeting of 100-win teams in the history of the Division Series, told us pretty much the same thing 162 games from April to September did — that the difference between the teams was the matter of a few swings of the bat and a couple of runs here or there (well, with the exception of Game 3’s blowout); that the Yankees had the superior bullpen and the Red Sox the superior rotation; and that, overall, the Red Sox were just a little bit better.

Aaron Hicks reacts after striking out in the eighth inning. (Elsa/Getty Images)

“None of these games are easy,” said Red Sox reliever Matt Barnes. “We’re going to have many more years of fighting [for] this division with them.”

After five solid innings from starter Rick Porcello, and perfect 1-2-3 innings from three relievers — including ace lefty Chris Sale in a surprise cameo — the Red Sox placed a three-run lead in the safest, most reliable place possible: the right arm of Kimbrel, one of the most dominant and steady closers of his generation.

But the Yankees, barely clinging to life, loaded the bases with one out on a single and a pair of walks, then scored a gift run when Kimbrel hit Neil Walker on the top of the foot with a slider. But as the crowd of 49,641 stood and begged for a comeback, Sanchez’s skyscraping blast to left fell just shy of the wall — a sacrifice fly that pulled the Yankees to within one. And when Kimbrel got Torres to ground to third, and when the replay confirmed the outcome, the Yankees’ season had met a sudden and wrenching end.

“He wasn’t the usual Craig Kimbrel,” Red Sox Manager Alex Cora said. “But he got three outs, and he closed out the game.”

“Just missed winning the game,” Yankees Manager Aaron Boone, who knows something about epochal home runs in October, said of Sanchez’s long flyball.

As one Red Sox pitcher after another mowed the Yankees down Tuesday night, the realization slowly settled across an increasingly silent stadium: none of it mattered. The Red Sox were about to dance across the infield and spray champagne in the visitors’ clubhouse for the second time in three weeks, and it wasn’t going to make a lick of difference when Boone lifted his starting pitcher or how the Yankees chose to deploy their bullpen or how many home runs they had hit in the regular season.

None of it was going to matter because the Yankees’ history-making lineup, in the second week of October, had suddenly stopped hitting, and it was because of that, not to mention the Red Sox pitchers who shut them down, that the Yankees lost.

After hitting a record 267 home runs this season, the Yankees failed to hit any in Games 3 and 4, thus dropping their record to 10-23 this year, regular and postseason combined, when going homerless. Simply put, they depend on their ability to hit the ball out of the park, and when they don’t do it, they aren’t built to manufacture runs in other ways. When Didi Gregorius lashed a double off Porcello in the fourth, it represented the Yankees’ first extra-base hit since the seventh inning of Game 2.

“Definitely frustrating,” Boone said. “Credit to [the Red Sox] for being able to hold us down. But you don’t move on usually when you can’t get enough big hits. They just outplayed us a little bit.”

One night after Boone had his bullpen moves scrutinized mercilessly — the consensus being that he was too late in pulling his starter and too passive in deploying his better arms in what would become an ugly 16-1 loss — the Yankees, this time facing elimination, again fell behind in the early innings with the bullpen at rest. This time it was veteran lefty CC Sabathia, in what could have been his final game in pinstripes, being left in the game to give up three runs, all of them coming in the third inning.

Still, nothing Boone did or didn’t do with his pitching staff would matter if the Yankees couldn’t score. A great bullpen can’t carry home a victory if it is never handed a lead to protect.

In stark contrast to Boone, Cora could seemingly do no wrong these past two nights, his every move seemingly producing not just the desired result, but something extra. He inserts utility man Brock Holt at second base Monday night in Game 3, and Holt hits for the cycle. He puts Kinsler back there Tuesday night, and Kinsler hits an RBI double. He uses Christian Vazquez at catcher, despite the fact he hadn’t caught Porcello all year, and Vazquez sneaks a flyball over the wall in right against Zach Britton — his first homer since June 26 — to extend Boston’s lead to 4-0.

“It seems like every button he’s pushing is the right one,” said Barnes, who contributed a 1-2-3 sixth inning in relief of Porcello. “I think he’s got a great feel for the game.”

The first postseason matchup between these rivals in 14 years failed to produce the same outsized drama and melodrama of the storied 2003-04 ALCS meetings — at least until the final half-inning of the series. The biggest controversy was probably Boone’s bullpen management. The biggest sideshow was the awful performance in Game 3 by first base umpire Angel Hernandez, who had three safe/out calls overturned that night.

As fate would hate it, Hernandez was behind the plate Tuesday night, and encountered few outward issues, though Sabathia was critical of his performance afterwards. “He was terrible behind the plate today,” Sabathia told reporters. “It’s amazing how he’s getting jobs umpiring in these playoff games.”

At the final out Tuesday night, at least once the replay review confirmed it, the Red Sox converged near the mound and hugged each other. In their raucous clubhouse, they sprayed each other with bubbly and blasted “New York, New York” from the sound system — a cheeky reply to Judge, who was spotted departing Fenway Park blasting the same song following the Yankees’ win in Game 2.

“Nothing personal with him,” Cora said of Judge.

The Red Sox hadn’t come to create drama or provide history with another unforgettable chapter in baseball’s best rivalry. If they had it their way, Tuesday night would have been another low-key, drama-free win — and it almost was until the bottom of the ninth. The Red Sox were built to win a title. They were here to win three games and move on.

Next up for them: the Astros.