The segment, which aired during Tuesday night's episode on CBS: "Top 10 Signs You Will Never Throw A No-Hitter."
"I was pretty excited," said Weaver, who no-hit the Twins at Angel Stadium on Wednesday night. "Every time I'm at home, I watch Dave before I go to bed, so it's pretty cool to be on his show.
"He's just so laid back. His dry humor, I love it. I got a chance to do a little interview before we did the Top 10 and stuff, he asked me some questions, and it was cool. It was fun. A lot of fun."
Weaver was stationed in one of the Target Field broadcast booths for about a half-hour pregame, rehearsing and taping the Top 10. Weaver's Top 10 list included:
10. You wear a glove on both hands.
9. The altitude of the mound makes you dizzy.
8. You performed your own Tommy John surgery.
7. Your pitches tend to bounce.
6. You spend most of the game sipping cocktails in the players' wives section.
5. You can only pitch when no one's watching.
4. The last guy you struck out was Phil Rizzuto.
3. You're allergic to the rosin.
2. You're still not sure if you're a righty or a lefty.
1. Most teams don't let the mascot pitch.
"No. 1, before they changed it, was: You pitch for the Mets [which have never thrown a no-hitter]," Weaver said. "But I felt bad. Being a baseball guy, I can't say that."
Weaver read from the teleprompter and did not require any second takes, he claims.
But he was probably more nervous for this than he was at any point on Wednesday night.
"I was, until I had a chance to rehearse everything and get a feel for how they wanted to do it and stuff like that," Weaver said. "But as soon as you hear him in your ear and you get under way, it gets a little nerve-wracking."