On Aug. 1, “The Button-Down Mind of Bob Newhart” reached  No. 1 on the Billboard charts, the first-ever comedy album to do so, launching Newhart’s storied 60-year career, including the iconic CBS sitcoms “The Bob Newhart Show” and “Newhart.”

“I thought [‘The Button-Down Mind of Bob Newhart’] might sell maybe 5,000 albums. I would’ve been happy with that,” Newhart, 90, told The Post, on its 60th anniversary milestone. “I really saw it as an adjunct to stand-up, to maybe get four or five more people to come [to a club] because they’d heard about that album.

“And then it exploded.”

Less than a year earlier, Newhart was working part time and hoping for a career in comedy — with no experience and absolutely nothing to show for his efforts, save for being “the funny guy in the barracks” during the Korean War (he served from 1952 to 1954).

Now, he was the hottest comedian in America — with a fascinating “overnight sensation” story behind his meteoric rise.

“A friend of mine in Chicago, a disc jockey named Dan Sorkin, who was at WCFL, said to Warner Bros., ‘I have a friend of mine that I think is very funny,’ ” Newhart said. “They said, ‘Tell him to put something on tape and we’ll listen to it.’ So I put all three of my routines on tape — the Abe Lincoln sketch, the Driving Instructor and the Submarine Commander — and Dan played it for them and they said they’d like to meet me.

“So I met with Warner Bros., which was about to go out of business. All they had was the Everly Brothers,” he said. “They said, ‘We like your material, we’d like to offer you a recording contract.’ But we had a problem — I had never played at a nightclub . . . I had done one or two [stand-up gigs] for charities in Chicago. That’s all I had going. I mean, there was nothing.

“I’d graduated with a degree in accounting [from Loyola University Chicago] and all my friends were getting married and buying homes and having kids — and I was working part time at Christmas in one of the department stores.”

It took Warner Bros. “the better part of a year,” Newhart said, to find a club willing to let the novice stand-up comedian with no experience record his act (even with the contract). He landed at the Tidelands Club in Houston. “One of the first things you learn in stand-up, the first day if not sooner, is that you can’t show any fear,” Newhart said. “You’re in charge of the stage. That’s your stage and if the audience senses any reticence on your part, you’re dead meat.

“So I walked onto that stage in Houston with all the bravado I could command.”

It worked. Newhart’s best-known surreal routines from that first album included “Abe Lincoln vs. Madison Avenue” (Lincoln’s New York press agent giving him advice over the phone before his Gettysburg Address); “Driving Instructor” (a TV series imagining a conversation between a nervous driving instructor and his clueless client); and “The Cruise of the USS Codfish” (a nuclear sub captain addressing his crew’s gaffes, including “firing on Miami Beach”). (Newhart later revived his celebrated “phone routine” for the opening of “The Bob Newhart Show.”)

The album, subtitled “The Most Celebrated Comedian Since Attila The Hun” (Newhart’s idea), began to rise steadily on the charts through word-of-mouth (mostly college students) and Newhart’s fortuitous television appearances on the 1960 Emmy Awards and a guest spot on Jack Paar’s “Tonight Show” (Betty White was the other guest).

“The comedy clubs weren’t around then,” he said. “There was a big sea change in comedy. There was Mike [Nichols] and Elaine [May], Shelley Berman, myself, Jonathan Winters and Lenny Bruce. We all kind of happened at the same time and the humor was different than the humor before that, when there were a lot of wife jokes . . . and they had no relevance to college kids who picked up these albums, which were about their fears and their concerns about life.

“They would get the record albums and go to someone’s dorm room and get beer and pizzas and someone had a record player. Those were their nightclubs,” he said. “I think they really created that demand.”

Following his appearance on the 1960 Emmys, hosted that year by Fred Astaire, Newhart was invited onto “The Tonight Show.” “That was a big break for any stand-up,” he said. “They said, ‘OK, there’s a star out there. Walk on it and do your routine and when it’s over . . . Jack will either call you over [to talk to him] or he’ll applaud.’ If he applauds that means it didn’t go very well.

“So I stood there for what seemed like a lifetime and all of the sudden, Jack motioned me over.”

In April 1961, Newhart won three Grammys for “The Button-Down Mind of Bob Newhart” and its follow-up, “The Button-Down Mind Strikes Back!”: Best New Artist, Album of the Year and Best Comedy Performance, Spoken Word.

“They didn’t even have a category for comedy at that time,” he said. “It beat out [Harry] Belafonte, Sinatra and an Elvis album [‘Are You Lonesome Tonight?’] They kept calling my name and I kept walking up there and thanking them for the awards.”

“The Button-Down Mind of Bob Newhart” continues to resonate. Pete Campbell (Vincent Kartheiser) listened to it in Season 1 of “Mad Men” and, in the opening episode of “The Marvelous Mrs. Maisel,” Joel (Michael Zegen) ripped it off, regurgitating some Newhart bits in his (failed) bid to become a stand-up comic.

“Years later I was giving Richard Pryor a Lifetime Comedy Achievement Award,” Newhart said. “He was in a wheelchair at the time . . . and he looked up at me and said, ‘I stole your album. In Peoria [Illinois]. I went into a record store and put it in my jacket.’

“I said, ‘Richard, I get a quarter an album,’ ” Newhart said. “So he got a quarter from someone and gave it to me for my royalty.”