Finally, the Yankees can book their playoff spot.

With a 4-1 win over the Red Sox on Thursday night in The Bronx, the Yankees ended a two-year postseason drought by clinching a berth in Tuesday’s wild-card game.

It’s their first playoff appearance since 2012, when they won the AL East and were swept by the Tigers in the ALCS after Derek Jeter fractured his ankle in the series opener.

The next step will be assuring that game is played at Yankee Stadium, which they can do with a single win in Baltimore over the weekend.

And even though they’ll need a win to get into the ALDS, they sounded confident in the champagne-soaked clubhouse.

“We’re capable of beating anybody and winning it all,” Andrew Miller said after the 10,000th win in franchise history. “For some reason, we’re an underdog and we’re thought of as underachieving. We’re a really good team. We’ve got a really good chance to beat anybody and that’s what the playoffs are all about. Personally, I’ll take us against anybody.”

Back in late July, when the Yankees held a seven-game lead in the AL East over a seemingly average Blue Jays team, it seemed like their presence in the playoffs was inevitable.

But the realities of a long baseball season smacked the Yankees in the face, first with Toronto bringing in reinforcements before the trade deadline coupled with the season-ending injury to Mark Teixeira and the second-half fade of much of the lineup.

On a wet, frigid night that certainly felt like October — without the crowd — the Yankees relied on old reliables CC Sabathia and Carlos Beltran early on and then newcomers Greg Bird and Rob Refsnyder to prevent a fourth straight loss to Boston after squandering an opportunity to seal a place in the playoffs on Wednesday.

Sabathia, while still not the ace he used to be, continued his recent resurgence by fighting his way through five innings and allowing just one run.

Beltran’s opposite-field homer to right-center to start the bottom of the second gave the Yankees a lead they never lost.

A two-out single to left by Brendan Ryan scored John Ryan Murphy from second to make it 2-0 later in the inning.

Sabathia got Travis Shaw to fly to center for the third out with the bases loaded in the fifth to preserve a 2-1 lead with his 96th — and final — pitch of the night.

Adam Warren, back in the bullpen, tossed three scoreless innings before Dellin Betances closed the game in the ninth in place of Miller, who Girardi didn’t want to use after he pitched two innings in Wednesday’s loss.

With three games remaining on the schedule in Baltimore, the next step for the Yankees is ensuring the wild-card game will be played at home, as the Rangers, Angels and Astros battle it out for the AL West crown and the second wild card, and the Twins hang on for dear life.

The Yankees will need one more win or a loss by Houston to guarantee a game in The Bronx on Tuesday.

“Our job’s not done, but a lot of people asked me if we were going to celebrate tonight and I said ‘Darn right we’re going to celebrate’ ” Alex Rodriguez said. “We worked really hard for eight months to put us in a position to win a world championship.”

It’s been six years since the Yankees won one of those.

“My first couple of years, I probably took this for granted and assumed it was like this every year,” Brett Gardner said. “And after the last two years, I realize how hard it is to get there. This year had its ups and downs, but it doesn’t matter how you get there. It just matters that you’re there.”