BALTIMORE — The door is ajar.

Not, “Come on in, the party’s just getting started!” Not even, “Sure, what the heck, we’ve still got some time.” More like, “We’re throwing everyone out in a half-hour.”

But it’s ajar, undoubtedly. And for these Yankees, that constitutes progress.

Just as the Yankees took no pity on baseball’s worst team, the Orioles, the Red Sox’s long-awaited speed bump arrived. When the Yankees (83-47) finished off their sweep of the O’s on Sunday night, 5-3, in their final 2018 visit to Camden Yards, they pulled within six games — five games in the loss column — of the Red Sox (90-42), who suffered a 9-1 loss to the pesky Rays, concluding a three-game sweep at Tropicana Field.

The Bosox have now lost six of eight, during which time the Yankees have gone 6-1 to pick up 4 ¹/₂ games in the standings.

The Yankees, not surprisingly, pleaded apathy and ignorance Sunday.

“We’re not thinking about the Red Sox,” Sunday night’s winning pitcher, Luis Severino, said after the game. “We’re thinking about the Yankees winning games.”

“Haven’t looked,” David Robertson said, hours before he picked up the save. “Couldn’t care less.”

“Honestly, I don’t look at the standings until we get to September,” Dellin Betances said. “I know we’re a couple of days away. From playing with [Derek] Jeter, he always told me he never pays attention until early, middle September. It’s something that I kind of got from the best.”

“Today, today, today,” Aaron Boone said, flashing his own smile. “Honestly, that’s how I treat it. When the Red Sox lose, it’s nice. When they win, it’s kind of, ‘Ho hum. It’s what they’ve done all year.’ But I don’t really get caught up in it, or it doesn’t really affect me emotionally one way or the other. What I see, this is us taking care of our business. If we do that, we’ll hopefully put ourselves in a good spot come the end.”

As of Sunday morning, the website Fangraphs gave the Red Sox an 88.7 percent chance and the Yankees an 11.3 percent chance of capturing the AL East. That swayed from Red Sox 91.3 percent, Yankees 8.7 percent Saturday morning as a result of the Yankees’ doubleheader sweep of the O’s and Boston’s loss to the Rays.

Historically, it simply is not easy to overcome this sizable a deficit with so few games left. Last year, with 130 games under their belt, the Yankees (70-60) trailed the Red Sox (74-57) by 3 ¹/₂ games, three in the loss column. The Yankees stepped on the gas the rest of the way, going 21-11 — and they finished two games behind the Sawx, who closed out with a 19-12 mark.

If the Yankees duplicate that 21-11 mark down the stretch, the Red Sox, who are on pace to finish 110-52, would have to tumble to a 13-17 record in order to give the Yankees the division outright.

The last time a team overcame a loss-column deficit of five or more games to win a division at the Yankees’ 130-games mark occurred in 2010, when the Giants, 72-59 on Aug. 29 of that season, climbed over the Padres (76-53) to capture the National League West.

However a certain hope surely exists when you regain control of your destiny, and that’s what the Yankees did Saturday and advanced Sunday

“We’ve got six games against them,” Betances said of the Red Sox. “That’s all I know.”

Before Saturday, the Yankees hadn’t controlled their own destiny since Aug. 3, when they dropped the second of four straight to Boston at Fenway Park and fell six games back in the loss column (7 ¹/₂ overall).

“If we play well, the way we’re capable of, as we get guys back, we’re capable of being a special club,” Boone said.

Special enough to mount a September surprise? Probably not. Yet after the Fenway Fiasco earlier this month, that it ranks as a topic of discussion at all marks a small triumph for Boone and his guys.