With a nice breeze blowing in The Bronx and the worst of the summer heat just a memory, Sunday felt like an appetizer for the fall to come.

And in a game and in a series that mattered, the Yankees played like a team that is hungry and ready for October baseball.

They finally uncovered several offensive answers for lefty Boston pitching. They entrusted one of the larger games of the season to a struggling Will Warren, who responded by authoring his best start of his year. And by the time it was winding down, the embarrassed Red Sox asked a position player to serve as their mercy-rule pitcher.

If on Friday and Saturday night the Yankees did enough to steal two of the first three games of the series, on Sunday they did everything in a statement, 16-1 demolition of the Red Sox in front of 45,256, who left the park with a better chance of seeing playoff baseball in The Bronx than when they had entered.

Because with the victory, the Yankees (78-59) clinched the tiebreaker over the Red Sox (74-63) by winning the season series, 7-6. Officially up four games for the top wild-card seed, the Yankees are effectively ahead by five because if the two clubs finish atop the wild-card standings with the same record, the Yankees would host the best-of-three, first-round series.

Of course, Aaron Boone’s group also took steps toward ensuring that tiebreaker won’t come into play and would prefer looking ahead toward the AL East-leading Rays, anyway.

The result — taking three of four and outscoring Boston, 26-9 — encourages. But so does the manner in which the Yankees took control, punctuated by a spotless finale.

Warren — whose ERA had risen from 3.45 to 4.39 over his previous 11 games, a span dating back to June 26 in which he had allowed 32 earned runs in 48 ⅔ innings (5.92) — looked like his excellent April self. He got into trouble in the first inning, allowing two of the first three batters he faced to reach, then retired the next 13 straight until a Trevor Story infield single in the fifth.

If nothing else, Warren looked like an arm who can see postseason innings in some form while holding Boston to one run over seven-plus innings in which he let up just six hits, walked one and struck out seven. His line would have looked even better if he had not returned for the eighth inning, when a double and an RBI single knocked him from the game and prompted a standing ovation.

For a while it felt as if Warren and Ranger Suarez — the fourth lefty starter Boston threw at the Yankees, though one was an opener — would duel deep into the afternoon. And then Suarez blinked against a Yankees offense that hit as it would like to in October.

In the breakthrough, five-run fifth, there were crushed knocks: José Caballero smacked a one-hopper to Story, who could not make the play, before Jazz Chisholm Jr. smoked a ball to right-center that was nearly robbed by a superman dive from Ceddanne Rafaela. Whether the center fielder caught it or not may still be up for debate, but replay could not overturn the on-field call of no catch.

And then there were massaged baseballs: Ali Sánchez, clinging to a roster spot and coming off a rough game in Saturday’s matinee, laid down a nice bunt that moved the runners over, before Paul Goldschmidt surveyed the drawn-in defense and knew he just had to make contact. The veteran softly grounded up the middle, the ball escaping into the outfield for a two-run single that left his bat at 68.7 mph.

And there were gone baseballs: Two batters later, Heliot Ramos, who has been a target of impatient Yankees fans in his short time in pinstripes, turned on a Suarez curveball and watched it land 416 feet away in the left field stands, his first home run as a Yankee a monster three-run blast that made it 5-0.

If fans did not immediately realize it was Ramos’ first with his new team, they probably realized as much as he rounded the bases. There were many chest pounds, some speed bursts and a few finger points as Ramos, who spent his first five seasons with the Giants, celebrated his first real moment in The Bronx.

Back-to-back shots from Austin Wells and Goldschmidt in the eighth prompted Red Sox manager Chad Tracy to ask infielder Andruw Monasterio to pitch, which went predictably with homers from Caballero and Wells (his second of the inning).

So a game that ended feeling like a March exhibition provided plenty of hope for the Yankees’ October.