The other day I read a New York Times piece in which Elisabeth Vincentelli extolled the virtues of Columbo, which ran on television in various forms from 1968 till 2003, and is now available on NBC’s new free streaming service, Peacock. It made me want to sample the show, an entire episode of which I had unbelievably never watched. (I guess I was more into Kojak, Harry O, and The Rockford Files.)

And then I came to this line: “In the episode “Forgotten Lady,” [Janet] Leigh is simultaneously chilling and poignant as a Norma Desmond-like older actress who rewatches her past oeuvre — including the actual Leigh movie ‘Walking My Baby Back Home’ — on a loop.”

Wait, what?!

As soon as was logistically possible, I had downloaded Peacock, searched for the episode, and pressed play. It was pretty amazing. As Vincentelli noted, it was in some ways a takeoff on Sunset Boulevard, in which silent film star Desmond (Gloria Swanson) lives in the past, in part through obsessive screenings of her own films (the ones we see are Swanson’s own). In “Forgotten Lady” — which originally aired in 1975 and was directed by Henry Hart and written by Bill Driscoll — Leigh plays Grace Wheeler, a former stage and screen musical star who hasn’t been in any shows for some time, for reasons not immediately clear but will prove important to the plot. Leigh was a mere 48 at the time and though Grace favors Norma Desmond–style caftans and cigarette holders (no headdresses, thankfully), she looks youthful and lithe enough to hoof it all night long.

As Vincentelli suggests, we’re meant to understand that she watches one of her movies every evening. Maurice Evans as the butler, Raymond, plays the Erich von Stroheim role and mans the projection booth.

As in Sunset Boulevard, we see Grace watching a Janet Leigh movie, Walking My Baby Back Home (1953). In it, Donald O’Connor plays an World War II vet who comes home and, in a classic case of terrible timing, wants to start a dance band. The plan inevitably fails but at least he gets the girl, Leigh’s Chris Hall. (Interestingly, in “Forgotten Lady,” her character in the film is referred to as “Rosie” — which is the name of Leigh’s character in another movie, Bye Bye Birdie.) From the clips seem throughout the episode, Walking looks fun enough but surely the reason it was used is cost: it and Columbo were both Universal productions.

I found “Forgotten Lady” fascinating (not surprisingly) because meta self-consciousness runs through it. Photos of Grace — Leigh at various stages of her career — abound in the home she shares with the gone-before-the first-commercial husband, Dr. Henry Willis (Sam Jaffe — who started out in the Yiddish theater, starred as Dr. Zorba on Ben Casey, pioneered the Jewish Afro, and deserves more than a parenthesis).

And there’s a book-in-movie aspect. Henry’s bedtime reading, which becomes an important plot point, is a novel called The Transformation of Mrs. McTwig. No such book exists, though the cover is a perfect rendition of a style favored by ’50s and ’60s comic novels, and an Internet sleuth has discovered that the plot description given in the episode also fits a real book, Paul Gallico’s Mrs. ‘Arris Goes to Paris (1958).

Another key plot point is that Raymond and his wife, the maid (Linda Scott), watch and relish The Tonight Show Starring Johnny Carson (on NBC, like Columbo), and director Hart gives us a generous portion featuring frequent guest Della Reese and Carson’s classic reaction takes.

The denouement of the episode is a second screening of Walking My Baby Back Home, to which Columbo and Grace’s old partner, Ned Diamond (John Payne — yet another old pro), have been invited. It’s a striking scene and the way Hart shows the film projected on Grace and Ned’s faces is a remarkable rendition of the way the movies have almost literally inscribed themselves on these characters.

Before you press play, two notes. First, Hart (understandably) cheats a little bit in having the sound from the movie suddenly and mysteriously muted as Grace and Ned have an emotional confrontation. (Surprisingly, this isn’t noted in the “Goofs” section of the IMDB entry on the episode.) And second, speaking of sound — you may want to mute the whole scene if you intend to watch “Forgotten Lady,” as I heartily recommend you do. As the saying goes, it contains spoilers.