Go to the source: Read the short stories by Charles Beaumont and Richard Matheson, some of which were the basis of TZ episodes (respectively, "The Howling Man" and "Nightmare at 20,000 Feet", for instance). Some of TZ was closer to science fiction than to fantasy/horror so you'll find they are a mix.
Slightly off from them, some short works of Saki, John Collier and Gerald Kersh might apply, may be precursors. Some Shirley Jackson might fit, too; I don't find it hard to imagine "The Lottery" as a episode of TZ. Maybe a bit closer to the mark, the short stories of Fredric Brown, and some later Robert Bloch -- from the '50s on -- might fit.
There are repositories of Unknown magazine on-line where you can sample some fiction from that time period. I feel like Beaumont and Matheson and maybe Serling were aware of that magazine since it set a tone for American fantasy that probably held for the next two decades. And when your list of writers include works by Brown, Heinlein ("The Unpleasant Profession of Jonathan Hoag"), Fritz Leiber ("Smoke Ghost"), Anthony Boucher ("they Bite") and others, you can't be all bad. Speaking of Leiber, the novels Conjure Wife and (the much later) Our Lady of Darkness, and Night's Black Agents, a story collection.
I second Jonathan Carroll, and some of his short work -- "The Sadness of Detail"; "The Panic Hand"; "My Zoondel" -- has a TZ feel, too. Some of Peter Beagle's work might also fit -- I'm thinking specifically of "Lila the Werewolf" which I remember as reading like something Woody Allen might have written after binging on TZ.
Added later:
And I just noted the word novels in the subject line. I refuse to remove the mention of short stories, though; that's where a percentage of the episodes originated.
