Conan O'Brien says he owes a lot to David Letterman.

On Wednesdays' episode of TBS' Conan, O'Brien recalled the pressure he was under when he took over NBC's Late Night from Letterman in 1993.

"I got the shit kicked out of me. Critics despised me, the ratings were bad, my skin broke out and my network started to make it clear that I probably wouldn't be around very long," O'Brien recalled. "I honestly have no ill will about that time because, by and large, people were right. I was in way over my head — and with this hair, that's saying something — and the conventional wisdom was that I should be immediately canceled."

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But four months in, Letterman called up and said he would like to be a guest on O'Brien's show.

"It was like the Beatles asking Maury Povich if they could stop by and sing a few tunes. At the time, I was convinced it was a prank — it couldn't be real. But, on February 28, 1994, David Letterman walked onto my set and blew the doors off the place. It's easily one of the happiest nights of my professional life," O'Brien said.

He went on to credit that night with saving his show.

"At one of the lowest points of my life, when I was a 30-year-old national punchline, Dave, for reasons I still don't really understand — completely rescued me. I truly believe that simple act of kindness turned everything around and made all the difference," O'Brien said.

Letterman ends his 33-year run on late-night TV on Wednesday on CBS. O'Brien said he will alert viewers to switch the channel to CBS the moment Letterman's Late Show begins. Conan airs at 11 p.m. on TBS, while Letterman's final show starts at 11:35 p.m. on CBS.