“Every generation needs their own songs,” Arlo Guthrie suggested to the hundreds who gathered at the Paramount Theatre on Thursday to hear him play “Alice’s Restaurant,” the 18-minute opus that launched him to fame a half-century ago. Grateful as he is that people still remember, he added, with a grin, “I don’t wanna be singing this for another 50 freakin’ years!”

Humor has always been a big part of Guthrie’s appeal, and “Alice’s Restaurant” is Exhibit A, a surreal tale based on a real-life experience of getting caught dumping trash in Massachusetts when he was a teen. “If I ever imagined that song getting popular, I would’ve made it a hell of a lot shorter,” he joked after another ramble through the marathon.

The thing is, it didn’t FEEL like a long song, to those of us in the audience. Guthrie has the story down so intrinsically by now, and it’s so much a part of his fans’ lifelong experience, that the minutes pass almost like seconds. He tweaked it just a tad on Thursday, allowing that the FBI fingerprint file on him would probably also contain text messages and e-mails these days. But it remains the piece de resistance of a masterful raconteur. And even as future generations write and adopt their own anthems, “Alice’s Restaurant” will roll on.

Austin got a show that was a little more special than some stops on Guthrie’s current tour, thanks to a significant local connection. His daughter Cathy Guthrie, who plays in the duo Folk Uke with Willie Nelson’s daughter Amy Nelson, lives here and came out to join the band for several songs.

That increased the number of Guthries onstage to four. Keyboardist Abe is a longtime fixture in Arlo’s touring ensemble, along with husband-wife Steve and Carol Ide (guitar and backing vocals, respectively) and drummer Terry Hall. But the ringer on this tour is Arlo’s youngest daughter, Sarah Lee Guthrie, an accomplished singer-songwriter in her own right.

Midway through the first set, Arlo turned the stage over to Sarah Lee for several songs that were among the show’s highlights. Remembering she’d last played this room two years ago for a tribute concert to Austin singer-songwriter Jimmy LaFave just three days before he died, she dedicated “Hobo’s Lullaby” — the title track of Arlo’s 1972 album — to him, inviting out sister Cathy to sing along.

Even more moving was a song she wrote about her mother, who died six years ago. Rendered almost solo at piano (with subtle keyboard adds by her brother Abe), it was a show-stopper, with lines such as “I’m in the wind and the rainbows, in the moonlight and stars” inspired in part by a vision her daughter had of Sarah Lee’s mother just after the passing: “She was an angel, and she was turning into a star.”

Between Sarah Lee’s spotlight set and the “Alice’s Restaurant” massacree — which featured footage from the 1969 quasi-documentary film of the same name playing on a screen behind the band — there wasn’t time for much more than just the most obvious hits and a few classics from Arlo’s dad, the American icon Woody Guthrie. Which was just fine, really: A steady diet of Steve Goodman’s “City of New Orleans” (Guthrie’s biggest hit, a top-20 single in 1972), Woody’s “This Land Is Your Land” and Arlo’s own gem “Darkest Hour” clearly satisfied the crowd.

And it’s a bonus when you can also tell stories about when you were a kid and 19-year-old Bob Dylan came to the house to visit your dad. “I liked him because he had weird shoes,” Arlo remembered, before launching into a gorgeous, graceful “Gates of Eden,” one of many Dylan classics that often gets lost beneath the weight of all the other classics he wrote. On this night, it was a welcome reminder that, while every generation needs their own songs, we’d do well to keep remembering the ones that got us here, too.