I don’t know my history of horror movies well enough to state if any other movies with that trope came before. I would, however, argue that while Jaws does start they way you describe, I consider it to be a very different movie than the horror movies you think it precedes. Other than that basic plot device, I think of Jaws as a thriller/action movie, not a horror/slasher movie, so the fact that they share that plot device doesn’t feel related.
Also check out 1974’s Black Christmas, the first of the “holiday”-themed slasher movies and a big influence on John Carpenter’s Halloween. (In fact, I read that Halloween was originally developed as a sequel to 'Christmas, but I’m not sure how reliable that is.) It has a good cast (Olivia Hussey, Margot Kidder, Keir Dulea, John Saxon) and is quite scary and atmospheric.
I believe the prototypical teen slasher movie was actually a Spanish film, La Residencia (1969). (Released in the US as The House That Screamed.) I recall seeing it as a wee lad and being deeply disturbed by it. I think you can watch that film and see that a lot of later teen slasher flicks borrowed heavily from it.
Of course, my knowledge of slasher flicks is hardly encyclopedic, so there may be other earlier examples.
(Sorry for the double-post, but I overlooked this one.)
Made in 1960, Michael Powell’s Peeping Tom is frequently considered to be the prototype slasher movie. If you get a chance to see it, do; despite being banned for many years in several countries and effectively ending director Michael Powell’s career, it’s a milestone movie.
More importantly, wasn’t this the first movie to use the now clichéd ’the calls are coming from inside the house’ bit?
Even if it wasn’t the first, it used it quite well. When the phone company guy finally gets a good trace, he tells John Saxon (the cop) the address and Saxon replies, “You idiot, that’s the address they’re going to!” and then the phone guy calmly just replies, “its also where they’re coming from”. And Saxon suddenly remembers being told earlier about the old extra line in the attic. And he doesn’t say all this, you just had to figure it out like he does.
Then the naive rookie cop (the one whom Margot Kidder played the ‘fellatio-6’ phone exchange joke on) is told this, and then told to call the house and get them to leave but without freaking them out by telling them the killer is there. And he’s so unexperienced he eventually breaks down and does tell Olivia Hussey (schwing!!) that he’s there.
Sounds really corny now, but it was cool 30 years ago.