Desree said:

Seven. Seven's plot was entirely dependent on the killer getting caught. I'm certain there are earlier examples though..

Good point.

Not quite the same as the evil super-nemesis thing as Spacey only turn up at the last minute, has no plan to escape or even any real plan beyond his capture. His game of chess is over the moment he turn himself in, he just sits back and watches it play out. Though I suppose the back seat of the cop car is a sort of mobile glass cage where he can sit and do the customary crowing about the brilliance of his plan.

If that counts, it's 1995, can anybody do earlier?