Sunday might have been the most encouraging day for Aaron Boone’s club since Aaron Judge had two pain-free big toes.

Judge hit, and then the Yankees followed the captain’s lead.

After Judge swung against Jonathan Loaisiga in his first time facing live pitching since he went down in early June, the Yankees’ lineup kept up the momentum.

The Yankees poured on four runs in the first inning en route to an 8-5 victory over the Royals, completing a sweep in front of 44,130 in The Bronx.

The Yankees (53-47) have won three games in a row for the first time since they won four straight from May 27-30, when Judge’s bat was still carrying the team.

“It’s no secret we’ve been struggling,” Boone said after the offense broke out following a dismal road trip. “To come home and regroup and get a series sweep … we still got a long way to go. We feel like we have a chance to be a really good team.

“We’re incomplete without question, but we do feel like there’s some things on the horizon that are going to fortify us.”

On an all-around excellent day for the club, the biggest negative development involved the Royals (28-73) leaving town, with the Yankees next hosting the Mets for two games.

After scoring seven runs in three losses in Anaheim, the Yankees bounced back against poor Kansas City pitching for 18 runs in the sweep.

Sunday starter Jordan Lyles entered with a 6.05 ERA and left with a 6.19 mark.

Previously, the Yankees had not been able to hit even struggling pitching.

On an afternoon of encouraging at-bats, Anthony Rizzo’s connections loomed particularly large.

The ice-cold slugger knocked his first home run in more than two months and finished 4-for-4, spraying an RBI double to left-center in the first inning, two singles through the middle and pulling a 364-foot shot to right.

“Sometimes something clicks. Definitely my first at-bat today, felt really good,” said Rizzo, who had last homered May 20. “You get a couple hits, and you start getting more belief that you feel right again. You just want to keep that feeling — bottle it up and never lose it.”

In the 45 games between homers, Rizzo hit .182 and struck out 46 times in 165 at-bats, a stunning downturn through a largely Judge-less, critical segment of the season.

The first baseman has tried anything to snap out of the funk, including abandoning his batting gloves Saturday, which returned Sunday, and turning to Taylor Swift’s “… Ready For It?” as a walk-up song Sunday.

Maybe his cruel summer is ending.

Rizzo smoked a Lyles sinker in the eighth pitch of his third-inning at-bat for the homer, then returned to a dugout that ignored him.

The Yankees gave Rizzo the silent treatment as he bounced his way through the dugout until his teammates exploded with joy.

“We got Rizzo back,” said winning pitcher Luis Severino (three runs in 5 ²/₃ innings), who was solid outside of a two-run homer from Michael Massey in the sixth that ended his day.

The team-wide positive signs began immediately.

The Yankees scored four runs in a five-hit first inning.

Jake Bauers, in his first game off the IL, singled and then strolled around the bases as Gleyber Torres — who later exited with a tight hip — blasted his 16th homer of the year.

Giancarlo Stanton’s bat continued to show life with a single before he scored on Rizzo’s double.

“A lot of great at-bats. A lot of tough outs,” said Stanton, who went 2-for-4 for a second straight day. “That’s what builds games like this. … Just got to keep going.”

The Yankees’ bullpen was dented in the ninth inning, when Ron Marinaccio allowed two homers, but otherwise pitched well — with some help from one more positive Yankees sign.

In the seventh inning, Nick Pratto smacked an Ian Hamilton four-seamer to deep right-center, but Harrison Bader was on the move.

Making his first start since he was drilled in the ribs Wednesday, the center fielder sprinted back, reached up at the warning track and smacked against the wall with a fully upright left arm, robbing Pratto of extra bases.

“If you can walk, you can go out there and play a baseball game,” Bader said. “Put it all aside and get ready and battle for a win.”

The Yankees tacked on three eighth-inning runs for some breathing room.

As Judge nears a return, perhaps the club is beginning to breathe again.