So I know the difference between 'brought' (bringing something, past tense of 'bring') and 'bought' (buying something, past tense of 'buy'), but I'm having trouble deciding which to use for this line: 'this brought/bought them the time they needed to escape.' Could someone please enlighten me? Thanks.
I'd go for "bought" - because you buy time, don't you? That's the idiom, that people are buying time. So it stands to reason that it should be "bought them the time...". Also, it's a trade-off - presumably they did something in order to increase the time that they had, so where it's a trade, it's an act of buying, hence bought.
I agree with Mckk. You could also say this"gave" them time. More passive; they don't have to do something to 'buy' the time. A subtle difference.
I actually question the need for the sentence at all. It screams "telling" us something and not showing us. Whatever it is that happened, it should be obvious that it created the opportunity (and time) for escape. Presumably you wrote the event, then you wrote the escape. The readers will know that the event enabled the escape.