Wrong show and wrong actress, but you've got the plot details spot-on.
"Lamb to the Slaughter" was an episode of "Alfred Hitchcock Presents" (which is the other anthology show people think of after "The Twilight Zone") that aired April 13, 1958. It starred Barbara Bel Geddes, not Shelley Winters -- Geddes is best remembered now as Ewing family matriarch Ellie on "Dallas."
Hitchcock is often referred to as "the master of suspense," but the suspense here doesn't come from mystery -- we already know who the killer is. Rather, this episode is rich with Hitchcock's other mastery: dramatic irony.
That is, if you remember your high school English lessons, the phenomenon where the audience knows something important that some or all of the characters do not. Hitchcock was a big fan of it (see also: "Rebecca," 1940, "Psycho," 1960).
In an interview, Hitchcock described the desired effect of this particular tool. "The audience is longing to warn the characters on the screen: 'You shouldn't be talking about such trivial matters. There's a bomb beneath you and it's about to explode!'"
The bomb is a hypothetical example, but Hitchcock's stories are littered with situations that the audience knows will blow up on the characters at any minute.
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