Then Letterman proceeded to take viewers, and television, on an extraordinary journey that was part confessional, part entertainment and wholly, if jarringly, hypnotic.
The medium has come close to moments like this before — Hugh Grant's prostitute mea culpa on "Tonight" is the familiar example of recent years — but never achieved the merger of farce and drama that Letterman finessed.
"I'm glad you folks are here tonight," he told his "Late Show" New York studio audience Thursday. "I'm glad you're in such a pleasant mood, because I have a little story that I would like to tell you and the home viewers as well."
"Do you feel like a story?" Letterman asked amiably, as if making sure a child was ready for a cozy bedtime tale.
The audience got much more than that from a man acknowledged to be a master of the art of broadcasting.
By turns raffish, somber, self-effacing, blunt and coyly, comically manipulative, Letterman wove a mystery tale of his own behavior and that of a CBS' "48 Hours" employee arrested in an alleged multimillion-dollar extortion plot against him.
Letterman took his time — 10 minutes, a TV eternity these days for one topic — to slowly reel in viewers.
President Richard Nixon's famed "Checkers" speech, so old-school in its clumsy sentiment as he fought to remain on the GOP ticket as vice president, had nothing on this.
Even the 21st-century pipelines that allow the famous to control their message, whether Twitter or Facebook or you name it, looked like amateur hour.
Opening his tale, the 62-year-old Letterman said it all started with a letter and package left in his car.
"I know that you do some terrible, terrible things and that I can prove you do some terrible things," the letter warned, with proof enclosed, he recounted.
The audience, expecting the comedy that's reliably delivered by Uncle Dave, played along. They laughed.
They laughed about the man who allegedly threatened to put this "terrible stuff" about Letterman's life in a screenplay and a book. They laughed when he recalled the district attorney's office telling him, "Hellooo, this is blackmail."
The first break in the levity came when Letterman finally disclosed how much allegedly was demanded for silence, a princely $2 million. Real money, even for a well-paid late-night host.
"Oooooh," breathed a respectful studio audience.
Letterman started to edge away from the light and into darkness. He feared being harmed, he said.
"I want to reiterate how terrifying this is," he said, almost plaintively, a private man forced to bare his soul. "I'm motivated by nothing but guilt. I'm a towering mass of Lutheran Midwestern guilt."
The audience, sensing its cue, applauded.
He had them on the hook, ready to deliver the big plot twist that would wow them — or turn them against him. Viewers knew there was something "creepy" that Letterman had done, because he kept saying that was part of the goods someone had on him. Letterman, a careful wordsmith, repeated "creepy" enough to make sure it stuck.
Even a devoted fan could easily summon the specter of the most awful transgressions. Then Letterman dropped his bombshell: There were allegations that he had sex with women who worked for him.
Finally cowed by an unvarnished, unfunny remark, by the suggestion of improper behavior, the nasty whiff of sexual harassment in the workplace, the studio audience murmured uneasily.
Letterman made his final, brilliant move. He was honest.
"My response to that is, yes, I have. I have had sex with women who work on this show," he said. Married since March to a girlfriend of many years, and the father of a son born in 2003, Letterman didn't say when the encounters occurred.
The comedian, who has mocked so many celebrities for such transgressions, suddenly was himself a target. But the audience was back on his side and erupting in applause and cheers.
Letterman moved gracefully into the role of victim.
He invoked his need to protect the women involved, his family and himself. He ended with — shades of Nixon — his hope that he can "protect his job."
"Thank you for letting me bend your ears," he said. Then, back to the business at hand with guest Woody Harrelson.
"Good to be here on this auspicious night," the actor said with a sly but good-natured smile. All was well with "Late Show" and its host.