The Cure is taking a victory lap.

The post-punk goth icons were inducted into the Rock and Roll Hall of Fame this year and arrived Saturday night at the Austin City Limits Music Festival with nothing to prove — and a wonderfully fleshed-out greatest hits set in tow.

“This is our last show of the summer,” singer Robert Smith said before a bouquet of seven encores. “We’ll be back. ... This is our popular music bit.”

Thirteen studio albums in, the band checks all the hit-making boxes that go into the ACL headliner calculus. Like Guns N’ Roses, they have a set built around four globally known monolithic properties (“Lovesong,” “Just Like Heaven,” “Friday I’m in Love” and “Boys Don’t Cry”). They also boast beloved and oft-imitated tracks from classic releases, a second tier of smash hits like “Close to Me” and “Why Can’t I Be You?” and the right personnel to blow it to bits live.

THE CURE WEEKEND ONE: Read our review

Keyboardist Roger O’Donnell and drummer Jason Cooper are long-tenured members; guitarist Reeves Gabrels has been a latter days regular since 2012 and is a former David Bowie player; and O.G. bassist Simon Gallup was tonight replaced by his son Eden.

“If only I had a son,” Smith deadpanned, introducing him.

Smith is in peak form as as a vocalist. Second number “Pictures of You” was so spot-on I had to squint to make sure he didn’t have backing tracks. The 60-year-old is that guy at the gym who only moves when he needs to and keeps winning with top-notch racquetball placement. “Shake Dog Shake” was a hard-rocking, loud resignation letter. Everyone stopped to film “Just Like Heaven” on their phones like tourists at Sea World, its graceful melody something to be appreciated via documentation.

But this set is refined and we know it’s good. It’s also been on standby across recent performances that all boast similar set lists. Between ACL dates, the band took it to Mexico City. They played a similar bundle of tunes here in 2013.

In terms of scheduling conflicts, neutral music fans were faced with the toughest headliner decision since Beck vs. OutKast in 2014 as Childish Gambino played opposite the Cure, in what Donald Glover said was his last show under that moniker. By performing with the hunger of a showcasing buzz band at SXSW, the Cure surely left Zilker with new fans. Not bad for a band that released its first record 40 years ago.

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