It was never the case that some apelike creature gave birth to a mutation that was fully human and she happened to be lucky enough to meet someone with the exact same mutation in her lifetime.
I agree I over-simplified evolution to the point of absurdity but your suggestion that "it works through tiny tiny changes over long periods of time" is by no mean a consensus among evolutionists. The theory of punctuated equilibrium, popularised by Niles Eldredge and Stephen Jay Gould, is one of several alternative theories accepted by many. But the thrust of this thread is the role of DNA :
OK, you've got the idea of mitochondrial Eve completely wrong...There was nothing special about "Eve" within her own lifetime. She was one of many females living at her time, and there were a similar number of males. She is only important in that she happens to have becom the most recent common ancestor in the purely maternal line.
If you had bothered to read the article in talkorigins (http://www.talkorigins.org/faqs/homs/mitoeve.html) to which I referred you would not have felt the need to repeat this decription of mitochondrial Eve. The article clearly says that mE is the most-recent common ancestor of all humans alive on Earth today with respect to matrilineal descent. When she was alive, she was most certainly NOT the Mitochondrial Eve. The title at that time was held by a distant ancestor of hers. This process of theoretically tracing back mitochondrial Eves cannot be continued indefinitely because life and the human species is finite (this argument comes from Dawkins). Eventually, you would get back to a woman who had no mitochondrial Eve, who was Eve herself, even if she was not the alluring seductress imagined in poetry and art.