Letterman, in his first show since Carson's death last week at age 79 from emphysema, peppered his Monday night monologue with jokes Carson secretly wrote for him in recent months, the New York Daily News reported.
Former "Tonight Show" bandleader Doc Severinsen sat in with Letterman's band to play one of Carson's favorite tunes, "Here's That Rainy Day."
"I owe everything in my professional career, whatever success attained, to Johnny Carson," Letterman said.
Letterman said Carson "created the template" for the "Tonight Show" that everyone else is "secretly doing."
"The reason we're all doing Johnny's 'Tonight Show' is because you think, 'Well, if I do Johnny's "Tonight Show," maybe I'll be a little like Johnny and people will like me more.' "
Letterman got his big break on NBC late-night talk but left for CBS after Carson's 1992 retirement.