Paul Simon taping “Austin City Limits” on Thursday, May 12, 2016. Courtesy of KLRU-TV/Austin City Limits; photo by Scott Newton

As much as “Austin City Limits” has pushed to broaden its horizons in recent years with in-the-moment stars such as Kendrick Lamar and Florence + the Machine, part of its mission is to continue capturing unique performances by some of the living legends of American popular music. James Taylor’s appearance last fall was a prime example, and the show added another notch to its all-timers belt Thursday when Paul Simon and his nine-piece band visited ACL Live.

Simon was in town for a two-night stand at Bass Concert Hall, and he stuck around to make his first appearance on the longest-running music television program in history. Joking with the crowd that, like many who watch the show on TV, he always thought the trademark skyline was the real thing rather than a set backdrop, Simon seemed to thoroughly enjoy his two hours onstage. The highlights will be gathered for an hourlong broadcast when the show’s 42nd season begins airing next fall. (Unlike many of the show’s tapings these days, this one was not live-streamed.)

Simon stayed fairly close to the set list he played at Bass Concert Hall earlier this week, with a couple of exceptions. The iconic “Graceland” got the nod during a three-song main encore rather than “Late in the Evening.” And the deliciously spooky title track to Simon’s upcoming album “Stranger to Stranger,” due out next month, was a mid-set addition.

A second encore on Tuesday at Bass had featured the Simon & Garfunkel classics “The Boxer” and “The Sound of Silence,” but he played only the latter tune at ACL Live. The first half of the song was, sadly, marred by technical difficulties, with an occasional thumping sound distracting from Simon’s otherwise spectacularly pristine solo acoustic delivery. Simon didn’t do a second take; perhaps those thumps can be edited out in post-production for the broadcast.

Much of the credit for the stellar performances on all three nights of Simon’s Austin run goes to his bandmates, who did not get an introduction but included Austin’s own Joel Guzman on accordion, percussion, guitar and keyboards. The rest of the cast: Mark Stewart on guitar, mandolin, sax and more (we spotted recorder and didgeridoo); Mick Rossi on piano, other various keyboards and percussion; Vincent Nguini, guitar; Bakithi Kumalo, bass and percussion; James Oblon, drums, percussion and guitar; Jamey Haddad, drums and percussion; Andrew Switzer, saxophone and flute; and C.J. Camerieri, trumpet and french horn.

Set list:
1.  Proof (instrumental)
2. The Boy in the Bubble
3. 50 Ways to Leave Your Lover
4. Dazzling Blue
5. That Was Your Mother
6. Rewrite
7. Slip Slidin’ Away
8. Mother and Child Reunion
9. Me and Julio Down by the Schoolyard
10. Spirit Voices
11. The Obvious Child
12. Stranger to Stranger
13. Homeward Bound
14. El Condor Pasa (instrumental)
15. Duncan
16. Werewolf
17. Cool Cool River
18. Diamonds on the Soles of Her Shoes
19. You Can Call Me Al
20. Wristband
21. Graceland
22. Still Crazy After All These Years
23. The Sounds of Silence

Paul Simon and band taping “Austin City Limits” on Thursday, May 12, 2016. Courtesy of KLRU-TV/Austin City Limits; photo by Scott Newton