"The Invaders" is the fifteenth episode of the second season of The Twilight Zone, and was first broadcast in January of 1961. It was written by Richard Matheson, and starred Agnes Moorehead, as well as the voice of Douglas Heyes, who also directed. Since a discussion of this episode without revealing the twist would be of little interest, this review will contain spoilers.
The figure of Rod Serling introduces us to a poor, rural farmhouse where a weary-looking woman is preparing a stew. She hears a noise, and climbs up to the attic to find a flying saucer, from which two tiny aliens encased in spacesuits emerge. She attacks them, and they attack her back, leading to a silent, twenty minute long battle in the farmhouse. They have powerful weaponry and can hide from her, but her size and strength overwhelms them, with her finally destroying the flying saucer with a hatchet. We then hear one of the astronauts saying the race of giants on this planet is too powerful, and we pan over to see that the flying saucer is United States Air Force Space Probe One. A modification on a tomato surprise: we were the aliens all along.
To me, the episode is more interesting because of the set-up and production than the twist ending, which I think has been done in several other science-fiction stories. The second season opener, King Nine Will Not Return, also featured a minimalist set-up and was very suspenseful because of it. But this story goes a few steps further: there is never any other characters seen, and the one character doesn't even speak. Filling up 25 minutes with only one actress who can only emote through body language is quite a daring move, but I think this episode pulls it off. As for the surprise of the woman being an alien and us being the invader: it does leave a few questions. While she is silent because she can't speak English; the question of why she looks like a human, and lives in a house that appears to be in 1930s America, is something that is left up to the viewer to figure out, or else to ignore.