Let me be as blunt as possible with you.
No matter what you do, you are running a 90% probability of losing this friendship. Drunk or not, you've already gone way too far.
I do not automatically agree with the other posters in this thread that she's probably rather flighty and looking for excitement, however, this is also a situation of "She did this WITH me, how can I trust she won't do this TO me?" Try to let her down lightly; something like "I'm sorry, but I just can't do this to [best friends name here]. I was drunk/not thinking clearly that night... I'm sorry, but I don't think we should hang out any more."
And then follow through. Don't hang out, no matter how tempting it is.
Now, on the other end, you also have to save the friendship somehow. Obviously, there are two choices: Lie or tell the truth.
If you lie, and he finds out, then you're fucked. If you tell the truth, and he didn't suspect anything, and wouldn't've asked, then you just dumped this on your friend to relieve your own conscience. As I said, you're probably going to lose the friendship. There's no real way around that unless you invent a time machine.