Some among you doubted. Commenters thought it unlikely that a small spider could capture, kill, and consume a big ol’ cockroach. For you unbelievers, here is a video of a small spider, Steatoda (just like the ones I work with) capturing, killing, and consuming a fully grown cockroach.
Doubt no more! Those little spiders have persevered thanks to the virtues of venom and silk. And cleverness.