BALTIMORE — On one hand, you don’t get much more new school than removing a starting pitcher with two outs in the fifth inning and a lead.

Then again, what’s more old school than going multiple innings with a fireballing reliever?

Chad Green rewarded Joe Girardi for his faith Monday afternoon at Orioles Park at Camden Yards. Girardi hopes such faith results in a nasty October weapon.

With Green providing 2 ¹/₃ perfect innings of relief, the travel-weary Yankees pulled off their third straight victory, 7-4 over the Orioles, keeping the heat on the Red Sox atop the American League East and the many clubs nipping at their heels in the AL wild-card race. The Yankees’ vibe seems to change by the half-week, and they’ve now followed a home sweep at the hands of Cleveland with four wins in five games.

And in the converted starter Green, they have the kind of guy whose potential postseason impact excites them. Who compels Girardi to defy convention in order to get him in the game.

“I thought [Jordan] Montgomery pitched a pretty good game today, but I knew I had Chad Green rested,” Girardi said.

The rookie Montgomery shook off a rough start, having fallen in a 3-0 hole in the second inning, and owned a 5-3 advantage when he walked Manny Machado with two outs in the fifth. Up stepped Orioles All-Star Jonathan Schoop, whom Montgomery had retired twice on infield outs. Out came Girardi with the hook. Schoop flied out to right field, making him 0-for-7 lifetime against Green — Montgomery said afterward he was fine with his manager’s decision — and the right-hander cruised through the sixth and seventh innings, striking out four, to get the ball (and a lead expanded to 7-3) to David Robertson.

So continued the transformation of the guy who offered signs of encouragement last season, after the Yankees acquired him and Luis Cessa from the Tigers for lefty reliever Justin Wilson, but nothing quite like this: a 1.97 ERA, 90 strikeouts and 15 walks in 32 games totaling 59 ¹/₃ innings, with a 3-0 record after his win Monday.

“His control has been outstanding, and his fastball plays up out of the bullpen, and his slider has been good out of the bullpen,” Girardi said. “Similar to Dellin [Betances], it’s been simplifying. He doesn’t need to be a three- or four-pitch pitcher anymore. He’s just been a two-pitch guy, and it’s been successful for him.”

Actually, Green threw more cutters (seven) than sliders (two) Monday, as per Brooks, although Girardi is generally correct. Entering Monday’s action, Green had thrown 64.8 percent fastballs and just 39.2 percent last year, according to FanGraphs.

“That’s the mindset I have, knowing that I might only pitch to the lineup one time,” said Green, who tallied a 4.73 ERA in 12 major league games (eight starts) last season. “I have 40, 50 pitches to work with instead of 100.”

That fastball “just jumps at the end,” Austin Romine said. “He attacks guys, and he’s got a live fastball. He comes at you and lets it eat.”

Romine started behind the plate as Gary Sanchez started his suspension, negotiated down to three games, for his role in the Aug. 24 Yankees-Tigers brawl in Detroit.

The Yankees checked into their hotel here at about 3 a.m. after beating the Red Sox in a Sunday night game at home. They had sufficient motivation to write this one off. Instead, in front of a crowd replete with Yankees fans, they picked up a good win and mounted further evidence that Green can be something special next month.

If you’re wondering whether Green, who primarily started in the minors, has acquired a taste for bullpen work, he said, “Right now, I’m obviously happy where I’m at. But in the future, we’ll worry about that later.” That’s a “No,” and look: A year ago at this time, we thought Luis Severino would be best in the ’pen. It’ll resolve itself.

Green’s outstanding 13.65 strikeouts per nine innings ranks third on his own team, behind Dellin Betances (15.58) and Tommy Kahnle (13.92).

“It’s comforting to know we’ve got some guys who can miss bats,” Romine said. That Green has consistently done so for two-plus innings per gig makes him one to watch in the playoffs, which increasingly look like they’ll feature these Yankees. Thanks in no small part to Green.