Poké Ball only shakes once and the Pokémon is caught

Nevermind, I've obviously silly at looking things up. Looks like it's called "critical catching" and that this isn't a bug or anything.

It's new since Generation 5 (and appears in Generation 6). There's a slight chance where the ball will only shake on the ground once before capture.

Source

It's called a critical capture. This was introduced in Generation V and is documented in Generation VI on a sign hidden behind a Cut tree to the left of the entrance to Reflection Cave on Route 11:

Trainer Tips!

When catching a Pokémon, sometimes the Poké Ball you throw will rock only once. This is called a "critical capture," and the more Pokémon you catch, the more likely it will occur.

For technical information, see this Bulbapedia article.