The son of a Baptist minister, Jimmy Webb grew up in rural Oklahoma. It doesn’t sound like the kind of pedigree that would help create one of the great American songwriters, but that’s precisely what Webb became.

By the late 1960s, he had written such hits as “Up, Up and Away” (for the 5th Dimension) and “By the Time I Get to Phoenix,” “Wichita Lineman” and “Galveston” (all for Glen Campbell). He would go on to write songs for dozens of other big-name vocalists, including Frank Sinatra and Barbra Streisand.

At 67, he has trouble reaching the highest notes, but he can still play a mean piano, and he has to be one of the best storytellers in America. On Sunday night, he performed a 90-minute set at the Kessler Theater to a crowd that hung on every note in what amounted to a love fest. It was, however, a deserved love fest.

Webb’s alchemy of storytelling and music is so special that it’s not a leap to imagine it as a one-man Broadway play, not unlike Billy Crystal’s “700 Sundays.” Helping to make the evening even more special was warm-up act Grace Pettis, a former award winner at the Kerrville Folk Festival, whose lyrical ballads set the tone perfectly.

Webb opened with “The Highwayman,” and after the song, began telling his remarkable stories. He explained that, during the 1960s, songwriters turned increasingly to politics, though he did not — his way of noting that “Galveston” is not an anti-war song aimed at Vietnam.

He hasn’t always had success with radio stations, as he said in telling a wonderful story about KOMA, the big station in Oklahoma, refusing to play “Up, Up and Away” because they thought the subject matter was drugs. Webb’s ex-Marine preacher man of a daddy loaded up his Bible and a .45 and drove to KOMA, which had the song on the air in 15 minutes.

“It’s now part of the family folklore,” Webb said with a laugh.

He told terrific stories about “Mr. Sinatra,” who recorded “Didn’t We,” as did Streisand. Webb sang a gorgeous version of “All I Know” and offered a heartbreaking aside about Linda Ronstadt, who sang it as a duet with Webb on his 2010 album, Just Across the River. Ronstadt recently announced that she has Parkinson’s disease. As Webb said sadly, “This may be her last recorded song.”

He sang “Wichita Lineman” and did a one-song encore of the more-than-eight-minute “MacArthur Park.” And then he went to the Kessler lobby and signed autographs until every single fan had gone home.