Scottish electro-pop outfit Chvrches, stylized as CHVRCHES, excels at its craft — triumphant pop songs that launch into the stratosphere but wear their broken heart on their astronaut suit sleeve.

“We’ve played, like, 470 shows,” announced Chvrches frontwoman Lauren Mayberry four songs into the band’s second night at the Fox Theater on Tuesday — a mini-residency lodged between Coachella weekends and its third appearance in the Bay Area after October’s Treasure Island Music Festival and December’s Not So Silent Night. “It’s a well-oiled machine, but it’s not always the same.”

And the night ultimately was another pitch-perfect, stadium-ready set from the band. Chvrches’ live shows on its Every Open Eye tour are technically stellar, well-rehearsed from its intergalactic entrance — complete with a background of flickering wall strobes and an inscrutable, alien-like transmission — to the final echoes of its gargantuan stateside hit “The Mother We Share.”

Its performance of “We Sink” was all stadium-worthy grandiosity. Unrestrained from the confines of headphones and accompanied on stage by a dizzying fractal background, the song reached new sonic heights. But had the band committed to the kind of relentless, excessive audio-visual barrage song after song, the set would have lost much of its appeal.

Chvrches stands out among its radio-friendly, alt-rock peers, precisely because its sets aren’t pitch-perfect recreations of its studio offerings. The songs’ boundless energy are countered by their emotional resonance, and neither the band nor the audience ran out of steam by the set’s end because of the band’s tactful, tension-filled pacing throughout the night.

It helps that Mayberry wields a masterful stage presence, striding on stage and dancing exclusively with power positions and gazing deeply into the crowd’s eyes. And even when she wasn’t all triumph and poise, she still served as the emotional core of the band’s weighty anthems.

Fresh off performing the power-pop lament “Empty Threat,” Mayberry paced around the stage, seemingly befuddled. “Am I just tired or are there stuffed animals in the audience?” she asked. There were. And, for a solid five minutes, she prattled on about furries — about the awful time she had hugging the critters at Disney World, about whether or not their costuming “was a sex thing” and whether or not they could bring them onstage during their show.

They could, and they did.

Ultimately, Chvrches’ show went awry in the best way. Not only did the costumed individuals dance on stage for a song or three, but Mayberry shed the mystical, practiced veneer of the band’s well-rehearsed tour schedule to unveil something better: a live show with heart and just a bit of humor. She giggled her way through “Gun” after a grand entrance from the furries and apologized to the folks in the audience who wanted to sing along with her. Immediately after the song, she joked to the audience and her impromptu stage performers, “You do realize that, if the Republicans get into office, this shit won’t fly.” And she remained as approachable even if, by the time the furries stepped off the stage, she couldn’t muster up the enthusiasm to give them a hug goodbye.

It may have been an unintentional outcome, but the rest of Chvrches’ set dazzled with its hair down. Maybe it was because the band wound up performing its crowd-favorite hits right after its newfound furry companions stepped off stage, or maybe it was because multi-instrumentalist and occasional vocalist Martin Doherty took the starring role to perform fan-favorites “High Enough to Carry You Over” and “Under the Tide.” But with the pretense of perfection obliterated by the arrival, the night already felt like a resounding success.

By the time Mayberry walked to the front of the stage to perform the much-awaited “The Mother We Share,” her acapella-styled introduction felt all the more vulnerable. She teased it out, encouraging the crowd to sing along with her — an apology to the fans who may have expected the well-oiled machine of the typical Chvrches performance and a thank you to the fans who embraced the unexpectedness of this one.