“We’re three sisters from the Valley playing the Greek,” marveled Este Haim, one-third of the sisterly trio bearing their last name. “I’m ‘Stone Cold’ Steven Austin when it comes to emotion, but even I’m emotional.”

Indeed, the story of Haim could well be the rock variation on “La La Land,” as directed by fellow Valley denizen Paul Thomas Anderson (who actually was at the Greek on this night, filming the show for a possible concert film). We can see it now: Three nice Jewish sisters from the 818 begin performing as a bar mitzvah band with their parents, only to turn into international pop stars.

Appearing before an adoring sold-out hometown crowd, Danielle, Alana and Este — resplendent in red billowing shirts — alternately kvelled over and thanked the enthusiastic, 7,000-strong, largely female audience.

“You guys don’t understand how important tonight is for us,” said Alana before launching into the syncopated, R&B/funk rhythms of “Little of Your Love,” from their recent sophomore album, “Something to Tell You.” “Everyone said we couldn’t sell out the Greek.”

Lead vocalist and ace guitarist Danielle held down the center, bearing that anger, frustration and release in both her singing and playing while, flanked on either side, Alanna handled keyboards and percussion and Este — between them, they dominate the between-song wisecracks — engaged in her patented bass-face mugging. On nearly every song, the sisters engaged in familial three-part harmonies and traded off verses, recalling a similar genetic match in sisterly bands like the Roches and Wilson-Phillips.

The 16-song, nearly two-hour set, which featured the trio backed by keyboardist Tommy King and drummer Jody Giachello, offered selections from their first two albums, from the chugging T. Rex-meets-Fleetwood Mac power pop of “Don’t Save Me” (which ends with Este squealing, “I f—ing love you, L.A.”) to the clipped, click-clack rhythms of “Ready for You.”

Given the backdrop of the ongoing Harvey Weinstein scandal, “My Song 5” (“About a f—ing mother—er,” explained Alana) added significance to the evening’s themes of female empowerment, its “I’m not your honeypie” refrain set off against Alana’s pounding percussion and Este’s fuzz-toned bass riffs.

Este takes lead vocals on a rousing cover of Shania Twain’s cheeky 1997 hit, “That Don’t Impress Me Much,” substituting the more au courant “OK, so you’re Ryan Gosling” for the recorded version’s Brad Pitt. “Walking Away,” from the new album, placed the sisters’ joined falsettos over a solitary drum machine as the threesome showed off some synchronized dance steps. “Nothing’s Wrong” followed, with a perfectly executed call-and-response between Danielle and her two siblings over the pop-rock melody.

“Now the party’s started,” Danielle shouted. “I feel like we can kick it up a notch.” Este used the moment to free-associate, “My dream is to be on ‘Shark Tank,” she cracked, apropos of nothing. “I’m in love with Mr. Wonderful.” Alana then joked, commenting on the side view of Este’s nose on the big screen, “That’s a profile of your Jewishness.”

“Forever” featured Danielle’s choppy wordplay alongside some heavy strumming and Alana’s gurgling organ, initiating the first hand-claps of the evening with its attempts to pull the plug on a faltering relationship. “I’m tired of fighting the good fight/ If you say the word, then I’ll say goodbye,” crooned Danielle.

“The Wire” and “Falling” end the regular portion of the set on a feverish high note, both songs about moving on from failed affairs, with the latter offering a nod to Michael Jackson’s “Don’t Stop ‘Til You Get Enough” in its chorus.

For the encore, Haim reappeared atop the sound board between the Greek’s orchestra and loge sections for a three-song set that included an acoustic take on Tom Petty’s “I Won’t Back Down” (surprisingly not his Valley-based ode, “Free Fallin’”). Returning to the stage with the four-piece string section used by opening act Rostam Batmanglij (who co-produced three and co-wrote two of the songs on the new album), the sisters launched into “Found It in Silence,” then the gospel fervor singalong of “Right Now,” which concluded with the three alone on-stage pounding a drum kit in a confetti-strewn finale.

And as the sisters left the stage, they could feel secure in the knowledge that they’ll have a roaring hometown audience for years to come.