Apparently, the first story to claim this title appeared in the December 1948 edition of Thrilling Wonder Stories, one of those brilliant pulp sci fi mags with garish bug eyed monsters and big breasted space maidens on the cover. Fredric Brown’s two sentence story goes:

"The last man on Earth sat alone in a room. There was a knock on the door..."

But I prefer Ron Smith’s 1957 story, titled A Horror Story Shorter by One Letter Than the Shortest Horror Story Ever Written, which goes:

"The last man on Earth sat alone in a room. There was a lock on the door..."