James Taylor, Renée Fleming and Yo-Yo Ma have been on “A Prairie Home Companion.” But on Saturday, Paul Simon became the biggest-name musical guest in 40-plus years of Garrison Keillor’s radio program.

With the boss on hiatus writing, host-in-waiting Chris Thile became suitably in awe at the Fitzgerald Theater. When Thile started talking to Simon after they’d performed “Gone at Last,” Thile’s voice suddenly got high. So Simon needled him by responding with a playfully high voice.

There was no joking when it came to the music. Simon dusted off 1972’s “Duncan,” offered “Rewrite” (from his most recent album, 2011’s “So Beautiful or So What”) and delivered a world premiere of “Wristband,” a humorous ditty about not getting backstage access without the proper wristband even though he was the concert’s headliner.

Thile, his band the Punch Brothers plus guests Sarah Jarosz and Andrew Bird as well as “Prairie Home” music director/keyboardist Rich Dworsky accompanied Simon. Bird, known for his fiddling and whistling, even took a whistling solo on “The Boxer.”

When the two-hour broadcast was over, a stoked Thile coaxed Simon into an encore for the Fitzgerald crowd.

“This is as unrehearsed as the rest of the stuff,” said Simon, casually dressed in jeans, an open shirt over a T-shirt and a fedora.

The ensemble treated the crowd to “Me and Julio Down by the Schoolyard.”