If you have a friend who is already invited to the party you can ask him to ask her if you can be invited. Many party organizers are open to let their guests have their own guests.
Who should you ask and how?
There are multiple persons in your class who are invited, you don't want to ask more than two of these persons (ideally one), because you don't want to be "that guy" who asked everyone to be invited.
Ideally you'd choose someone who is: one of your close friends and one of her friends. When asking, I would not mention the fact that you want to get closer to the girl. People gossip a lot, and if she learns it that way, that could lead to an awkward situation you want to avoid. Also if it happens that someone else has views on the girl, he could try to prevent you from attending the party. Just say you'd really like to party on Halloween but you have nothing planned yet.
Be prepared for a refusal from either your friend (maybe he doesn't feel very close to this girl and wouldn't dare asking her this favor), or from the girl, it's her party, you are asking quite late and maybe everything is set up for a fixed number of persons and adding more would disturb the organization. Or maybe she invited only her close friends, etc. etc.
I've thrown quite a lot of (small) parties, and there are some in which I had no problem telling my guests they could invite who they wanted (but I always validate first to be sure my place is not going to be too crowded, or set up a limit for invitations).
And in some other occasions I only invited my closest friends and told them they couldn't invite anyone else because I wanted to see them and only them.
So even if you face a refusal, do not take it the wrong way, there might be a lot of reasons.