A day after their hopes of winning the AL East officially were dashed, the Yankees took a step closer to getting to the next best thing: hosting the wild-card game.

It was hardly without some unexpected drama, though, as the bullpen faltered in the later innings against the Orioles, who pulled to within a run in the eighth before the Yankees held on for a 10-8 victory over the worst team in baseball.

If the Yankees are going to hold off the Athletics for the top wild-card spot, they will have to continue to feast on Baltimore, but they nearly blew what should have been a rout, as little-used Jonathan Loaisiga and A.J. Cole each had brutal outings — as did David Robertson.

Dellin Betances, the Yankees’ seventh pitcher of the night, closed it with a scoreless ninth.

“That got a little dicey there,’’ manager Aaron Boone said. “We’ve got to be able to piece it together at times. Tonight wasn’t a great night for us in that regard, but I’m not overly concerned.”

Before the bullpen added unneeded drama, CC Sabathia tossed six solid innings and the Yankees opened a 9-4 lead into the seventh.

Sabathia gave up just two runs, then reiterated his desire to pitch again next season.

Before Sabathia — or anyone else — gets to 2019, there’s unfinished business this year.

The effectiveness of Sabathia’s cutter helped the veteran left-hander deliver his best performance since he faced the Orioles the last time on Aug. 24. He picked up his 245th career victory, tying Dennis Martinez for 51st on the all-time list.

“I thought everything was a little bit better today,’’ Boone said of Sabathia. “He was generating the weak contact we’re used to seeing from him.”

Didi Gregorius and Aaron Hicks both hit two-run homers off Baltimore right-hander Yefry Ramirez, who give up six runs in 3 ²/₃ innings.

The outcome seemed all but determined when the Yankees were up 6-0 through four innings and again when they were up 9-4 in the seventh.

Cole and Robertson each gave up two-run shots and suddenly the Yankees, who maintained their 1½-game lead on Oakland for the top wild-card spot, were in trouble.

But Robertson got out of the inning and Aaron Judge delivered a run-scoring single in the bottom of the inning to make it a two-run game before Betances finished it with his fourth save.

The victory allowed the Yankees to reduce their magic number for clinching a playoff spot to two, as the Rays also won on Friday.

Still, it was hardly an overwhelming performance.

“We were able to outlast them,’’ Boone said.

The Yankees have two more games against the Orioles at The Stadium before they visit the relentless Rays in St. Petersburg, Fla., for four games and then end the regular season with three games against the Red Sox at Fenway Park.

It remains to be seen how Boston will treat that series, but the Yankees have a number of goals to reach over the final week-plus of the year.

Boone said he’s confident there’s room between now and Game 162 for the Yankees to get the ship righted.

“I think it’s enough [time],’’ Boone said before the game. “Ultimately, we’ll see, but I absolutely believe it’s enough.”

Sabathia added: “I think we’re playing as good as we can.”

And he agreed the Yankees will find their stride in time for the postseason.

“We’re whole again,’’ Sabathia said, pointing to the return of Judge and Aroldis Chapman from injuries in the last week. “The more games we play, the better we’ll be.”