I agree this is of the best scenes in the series, and it really helps the episode be one of the best, IMO.
I also think the scene where Columbo gets angry with Joan Hudson is a defining moment. Often maligned as behavior of the character that was abandoned, I like to think of it as a character that evolved in later episodes. The outburst at Dr. Mayfield and the scene with Dr. Borden in a Deadly State of Mind, for example, reveal that part of Columbo that aligns with the “Hey, I’m not messing around” aspect of his personality as it drives his profession.
The whole episode has a fresh-out-of-the-box spirit. Sure, the Columbo character will be honed by Falk as the series progresses (even overwrought at times in later years) but this pilot is in a class of its own. As has been pointed out, check out Falk and Natalie Wood in Penelope – the baseball-bubblegum scene – for more of the good, early stuff.