The famous final shot of Jaws has Brody (Roy Schieder) and Hooper (Richard Dreyfuss) paddling on a piece of wreckage from the Orca back to shore after killing the shark, a simple and lovely character moment that ends the movie neatly and decisively.

Alexandre Aja's Crawl does something similar but even more stripped back. The thing that ends the movie and seals the characters' fate (good or bad, I won't spoil which) appears and the credits immediately start to roll against the strains of Bill Haley and the Comets' See You Later Alligator.

Coming at the end of the movie it's hardly a statement of creative intent for everything that's come before, but it symbolises everything it seems Aja was going for beautifully. This is a straightforward, no fuss monster movie that does exactly what it says on the tin and wastes no time doing so.

The script establishes enough about Haley (Kaya Scodelario), her sister Beth (Morfydd Clark) and their father Dave's (Barry Pepper) relationship while setting up the concept. It's deep in the tropics of Florida (actually shot in Serbia, of all places) with a hurricane closing in. A student and competitive swimmer, Haley is slightly estranged from her Dad, who insisted on staying in the house the family grew up in even though everybody (including the girls' mother) left.

But with clouds gathering, rain peling down and unable to raise her Dad on the phone, Haley drives into the all-but abandoned old neighbourhood to see if he's okay. After a protracted sequence of looking for him Haley finds him in the crawlspace underneath the house, injured after being attacked by an alligator that's still in there with them.

It starts a story constructed of a decent number of inventive set pieces that are well designed and executed and carry you through the economical running time at a very appreciable clip.

Whether it's the sewer pipe that will lead them to freedom (but take them past a huge, sludgy alligator's nest first), the robbers looting the gas station down the road who's attention Haley desperately tries to get before they meet their awful fate, the water rising or the childhood friend and cop who you think will finally save them when he arrives, every one of the pair's adventures is gripping, tense and plausible in the context.

But lest you think it's an exercise in verite realism, you also have Scodelario with her hand in one of the hungry monster's mouths, it trying to remove her arm from her body and her screaming as she unloads the clip of the gun she's carrying into its brain. Later, she traps a full grown attacking alligator in a shower to escape the bathroom it's likewise got her trapped in.

The script by Michael and Shawn Rasmussen also manages a delicate balancing act in raising the stakes. The thing about huge carnivores is that you assume if they get hold of you it's all over, but both Dave and Haley end up in gator jaws several times, sustaining injuries but getting away and the film not only makes you believe they could have done so but somehow doesn't let the urgency evaporate. If alligators get you but don't kill you, are they really that dangerous? And if the entire movie is about them trying to get you and failing, is it really a true horror movie? In each case, yes – as the writing enables.

The actors take it seriously enough to sell it and make you believe in what's really happening, and if you only know Aja from his work on the tongue-in-cheek Pirahna reboot series you won't realise how good at this sort of thing he is; you only need to look back on High Tension/Switchblade Romance (depending where in the world you saw it).

The whole thing was shot in a series of water tanks at a Belgrade shipping container storage depot, and the CGI not just of the creatures but the storm getting closer in the sky around them and the neighbourhood gradually falling further under the onslaught of the deluge are convincing and alive.

After his calling card in High Tension and his having been subsumed into the Hollywood machine to be a horror comedy hack for the Piranha series I'd assumed it would be the last we'd see of Aja as that subgenre fell out of favour, so it's great to see him do such a cool little creature feature in such a well defined genre.

And yes, it was such a successful horror thriller both economically as well as creatively a sequel's been announced.