For 5 ¹/₃ innings Thursday night, Gerrit Cole no longer was battling the Blue Jays for the game or his American League contemporaries for the Cy Young.

However briefly, he was competing with legends of the past for a place in baseball history.

Cole’s early bid for the 25th perfect game in MLB history fell 11 outs short, so he probably will have to settle for a Cy Young.

In an outing that transitioned to merely dominant, Cole began to put the finishing touches on a season that seems destined to end with the AL Cy Young Award, which would be his first in a brilliant, 11-year career.

The Yankees ace allowed one run on just two hits, struck out nine and walked none in eight innings during a 5-3 victory over the Blue Jays on Thursday.

An announced crowd of 37,646 in The Bronx witnessed more excellence from one of the few excellent Yankees in an otherwise lost season.

“I thought he was putting it where and how he wanted to all night,” manager Aaron Boone said of Cole. “That was him. I don’t know if it was his best stuff, but it was just so sharp.”

Cole recorded 16 straight outs to begin the game before Alejandro Kirk smacked a legitimate, hard-hit double to right-center with one out in the sixth inning.

The Yankees ace stranded Kirk before the Blue Jays pushed across their first run in 19 ²/₃ innings this season against Cole on an eighth-inning wild pitch.

After his 107th and final pitch to finish off the inning, Cole walked off the field and tipped his cap to a standing ovation from the crowd following his final start of the season at the Stadium.

“That was special for me,” said Cole, who entered the dugout and heard Boone tell him he was proud. “There’s just something about having good nights in The Bronx. It doesn’t get much better than that.”

Cole again stated he is not thinking about the Cy Young, even if he is queried about the award after each outing.

The right-hander is expected to have one more start, next week at Toronto, in which he can make a final statement, though it might not be needed.

He lowered his ERA to a league-best 2.75, which, according to Elias Sports Bureau, is the lowest by a Yankees starter through the first 32 starts of a season since Ron Guidry in 1978.

He stretched his innings pitched to an AL-best 200, hitting that milestone number for a second straight season and the sixth time in his career.

His competition for the AL award includes Minnesota’s Sonny Gray (2.84 ERA in 174 innings), Seattle’s Luis Castillo (3.06 ERA in 188 ¹/₃ innings) and Toronto’s Kevin Gausman (3.29 ERA in 178 innings, with a league-best 232 strikeouts), who shut down the Yankees for six innings Wednesday.

“All of us playing behind him are trying to back him up as best we can,” said Ben Rortvedt, a personal catcher for a Cy Young front-runner, “because we know there’s something special on the line.”

Behind Cole, the Yankees (77-76) avoided a sweep, powered by a three-run home run from Jake Bauers and RBI doubles from Estevan Florial and Aaron Judge.

Clay Holmes, though he allowed two runs (one earned) in the ninth inning, preserved the masterpiece by getting Spencer Horwitz, who represented the go-ahead run, to ground out for the final out.

Cole did not need much help from his supporting cast and did not want to become reflective before his season has concluded.

“All I know how to do is to get ready for the next one,” said Cole, who has lived up to his $324 million contract.

In four seasons in pinstripes, Cole has been precisely the stud the Yankees envisioned he would be.

After one more night that might not have been perfect, but surely was affirming, Cole took one step closer to what appears to be an award-winning culmination.

“It’s been everything you could have hoped for,” Boone said of Cole’s tenure with the club. “He’s been completely as advertised and what we hoped when we started the recruiting process and flew to California and met with him.”

“This is what you hope for.”