Say this for the Phillies: They will be relevant this summer.

That wasn’t a foregone conclusion two weeks ago. After an 11-1 humiliation on Memorial Day in Cincinnati, the Phillies were a season-worst four games under .500, five games out of first place, and had lost 12 of the last 17 games. The season appeared to be at a tipping point. They could pull it together and stay in the thick of a bunched-up National League East race or fade away before schools let out.

Consider this last week to be a statement then. The toughest tests still lay ahead, beginning this week in Los Angeles. But in closing out a wildly successful homestand with a gem from Aaron Nola (finally) in an easy, breezy 7-0 romp (at last) over a New York Yankees team that is in full-blown crisis mode, the Phillies made clear to the announced crowd of 38,512 -- the largest of the season -- that they aren’t about to fade away.

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“Baseball’s a weird thing. You start a new month and you almost feel like you can reset,” said left fielder Andrew McCutchen, who doubled twice and drove in two runs. “It’s like, ‘All right. New month. Here we go.’ It just sometimes works out that way, and yeah, we’ve been playing some good ball this month.

In going 6-2 against Washington, Atlanta, and Yankees, the Phillies, at 32-31, climbed above .500 for the first time since May 19, when they were 22-21. They picked up only one game on the division-leading Mets during the homestand. But they gained 2 1/2 games in the wild-card standings.

(And, no, when you’ve been absent from the playoffs for nine years, mid-June is not too early to pay attention to the wild card.)

“It’s big. Really big,” Nola said. “Especially with the Yankees coming to town, it was a big sweep, two-game sweep of those guys.”

For a change, the Phillies didn’t need last-at-bat theatrics. After three consecutive walk-off victories (two against the Braves and Saturday against the Yankees), they grabbed a four-run lead in the second inning with more top-of-the-order thunder from Odúbel Herrera and Jean Segura, tacked on three runs in the fifth, and let Nola do the rest in his sharpest outing in weeks.

Nola barely broke a sweat in 7 2/3 innings. Never mind that the Yankees had neither Aaron Judge nor Giancarlo Stanton in the lineup. He allowed three hits and one walk, struck out nine, and walked off the mound to a nice ovation in a confidence-building outing after posting a 5.68 ERA and failing to get out of the seventh inning in his previous six starts.

“It felt good to finally get back in the seventh, eighth inning,” Nola said.

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The Phillies put Nola back on his regular turn in the rotation after taking advantage of multiple days off to give him extra rest before his previous start. But he wasn’t sharp on six days’ rest last week against the Braves. So manager Joe Girardi changed course and had him face the Yankees rather than giving him an additional day of rest and starting him Monday night in Los Angeles.

Maybe it was coincidental, but Nola’s average fastball velocity ticked up to 93.4 mph, slightly higher than his season average of 92.7 mph.

“He’d had a lot of days off and maybe that was contributing to it,” Girardi said. “He wasn’t getting on the mound enough was kind of my thought after looking at some things. We’re trying to be proactive here because we worry about the back end, but sometimes maybe a guy gets out of his rhythm. I think he tweaked a few things, and this is what we got today. That’s the Aaron that we see all the time.”

Said Nola: “It felt good, actually. Seven days [off] is kind of like a college schedule. I haven’t done that since college. We’re used to every five games. Felt like I was just out there a few days ago. I like that. I like to pitch as much as I can.”

Nola took advantage of the Yankees’ aggressiveness early in the game. He had an eight-pitch first inning, aided by a ground-ball double play from Gleyber Torres, and a 10-pitch second. But he also commanded his fastball and got ahead with strikes, which didn’t allow the Yankees to work deep counts.

As much as Nola needed a game like this, the Phillies did, too. None of their flaws -- poor defense and a shaky bullpen, to name two of the more prominent ones -- is going away. But they played their most mistake-free game in a while and won their third consecutive series for the first time all season.

“It was just all-around good baseball,” Nola said. “The hitters came up big today, too. Put up seven runs pretty quick. Good plays in the field. Just a solid win overall.”

Herrera picked up two more hits, while Segura notched his third three-hit game in a row, joining Chase Utley as the only Phillies players to record three consecutive three-hit games in the 18-year history of Citizens Bank Park.

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“I joked with somebody today, I said, ‘Segura’s the Steph Curry of Major League Baseball. Just as easy as Steph hits a three, it’s just as easy as Segy gets hits,’” McCutchen said. “When [Herrera and Segura] are at the top and getting on base creating havoc, it definitely sets those 3-4-5-6-and-on guys, it sets them up to do some special things and drive them in.”

Now, though, comes a stiffer test, with 11 of the next 13 games on the road, where the Phillies are only 11-19 this season and 87-133 since the beginning of the 2018 season. It starts Monday night in Los Angeles against the defending World Series champion Dodgers.

“We just have to continue to keep doing what we’re doing,” McCutchen said. “We played three crazy games and were able to win comfortably today, so hopefully we can take that to the West Coast.”