Translation:It rained last night.
According to WWWJDIC, 夕べ can only mean "evening"; when used to mean "last night", it's primarily written in kanji as 昨夜.
So it depends on what you want the sentence to mean.
Actually, I don't think that is what WWWJDIC says; rather it says that "evening" can only be written 夕べ or 夕 (and "last night" is primarily written 昨夜). That is to say, 昨夜 can't mean "evening" but 夕べ can mean "last night", though that wouldn't be the most common way of writing it.
Is the [雨] strictly necessary in this sentence? Isn't that like saying it rained rain?
I think "furu" means "to fall" for example, "yuki ga furu" means "it is snowing". So yes, ame is required.
Also The fact that the rain will fall is understood, making the verb unnecessary, so it is often omitted. Therefore きのうは 雨 (が ふりました) でした Would also mean the same.
"Was raining" would be past progressive (降ってった), while this sentence is simple past ("rained"). I've seen different opinions in other comment sections about whether or not past progressive in English should still be accepted, and I don't know enough Japanese to have an opinion of my own. I just thought it might be a good idea to mention the difference between the tenses.
- So, it looks like ゆうべ has two rendering in kanji: Wiktionary
- One of these two kanji forms then has two readings: Wiktionary
- And the other is simpler pronunciation-wise, but more flexible in meaning: Wiktionary
So at the end of the day, my question is what time period does the kana form given here cover: something like 5 pm yesterday to dawn this morning?
And if you used kanji, 夕べ would go from 5 pm yesterday to midnight? And 昨夜 wouldn't pin the time down any more specifically than 5 pm-ish to dawn, but how you read it aloud would?