They are a living, breathing postseason team now.

They are a Big Boy team.

They are playing well at home. They are not buying the hype of the “new Yankees.’’ They have been able to come back from deficits and win games. They are winning games even when their ace, David Price, doesn’t quite have it.

Their bullpen isn’t giving leads back. Their hitters are coming through with big hits. They are scoring runs with something other than home runs and hits, though Xander Bogaerts’s 20th homer in their 6-5 victory over the Yankees on Saturday at Fenway Park was huge. The winning run scored on a wild pitch.

They have beaten the Yankees three straight. They have destroyed their wild-card dreams while enhancing their own divisional wishes. They are taking this difficult schedule and attacking it — darn, I can’t believe I’m writing this — one game at a time.

The Red Sox were behind, 5-2, but that didn’t seem like a great obstacle. Postseason teams don’t wobble when presented with modest deficits, especially at home. A couple of weeks back they may have. Maybe all of those one-run losses were unbecoming of a postseason team, maybe they woke up as a result and decided to lift that one-run burden off their shoulders. It was a win over the Yankees. A one-run win. Shout it from the roof tops.

“I wouldn’t just limit it to the last three games, but really the last three weeks,’’ said Red Sox manager John Farrell.

“I think we jelled even further by having to go out to the West Coast a couple of times, lengthy road trips. There was an inner belief within our group that began to grow and then three come-from-behind wins this week. Those are key games and not always in the most friendly situations against an elite closer, against tough lineups. This team has responded to the challenges we face.’’

This is a game they probably would have lost a couple of weeks ago. But they roared back. There was no panic. Come back little by little and then finish it off.

“The gradual fight, just keep coming from a lineup standpoint,’’ Farrell explained. “Build an inning, add a run, a big two-run blow by Bogie to get us closer. This was a little bit more methodical than one big inning and that takes contributions from guys who came out of the bullpen to the lineup.’’

Little things, too. The great throw by catcher Sandy Leon to nail Brett Gardner trying to steal second in the seventh inning with the Red Sox trailing, 5-4, was another outstanding play.

Even when Dustin Pedroia took a called third strike with the bases loaded in the sixth, trailing by a run, the Red Sox were not spooked by that missed opportunity.

It was a good week for big games. The Red Sox started this series with a walkoff win on Thursday, perhaps the most dramatic victory of the season. Sometimes, as Farrell has said, certain wins carry a little more weight, and that one certainly did.

They followed that with a win on Friday behind Clay Buchholz, and then on Saturday, Bogaerts, a guy we haven’t heard too much from during the second half of the season, homered and knocked in three runs. It was good for the Red Sox to hear his name called again.

The game featured Craig Kimbrel’s four-out save, Farrell leaving nothing to chance. And don’t undervalue what Price did by pitching two extra scoreless innings in a game he could have exited much earlier. By pitching shutdown innings in the fifth and sixth, Price set up his bullpen nicely and on a positive note.

All that’s left of this series is a Sunday night game that could result in a possible four-game sweep of the Yankees.

Yes, it took 148 games, but the Red Sox are toughening up and ready for the postseason.

After Sunday’s finale with the Yankees, the Red Sox will head to Baltimore for a first-place showdown. Then they go to Tampa Bay for what are always tough games against a team that could create problems because of its starting pitching. And then it’s back to the Bronx, where the Red Sox will have to stave off the Yankees once more, this time in enemy surroundings.

The season has had its ebbs and flows. Who knows if there’ll be another dip before all is said and done?

But there seems to be an inner confidence around the clubhouse, a good sign for a team that now has a playoff feel with only 14 games to go.

“It’s a good feeling,’’ said Hanley Ramirez, who went 3 for 4 and remained hot. “We have to keep playing hard and win games. We want to win this division and to do that we can’t leave anything out on the field. Our guys are playing hard and you can see the results. It’s fun, but we’re serious out there. We’re very serious because we want to win.’’

Ramirez is on a 6-for-8 roll and has 44 hits in his last 32 games. Remember the immaturity issues that plagued Ramirez’s past? All gone.

Ramirez and the team have come of age. It’s a Big Boy team, a playoff team.

Nick Cafardo can be reached at cafardo@globe.com. Follow him on Twitter @nickcafardo.