From my experiemce buying booze in Japan, you can either buy it from a) vending machines b) supermarket or c) convenience store. At supermarkets they can block you from buying stuff in the self-service section, but in convenience stores they just make you accept that you are 20 or older and that's it... I guess a clerk at graveyard shift won't be so anal about it, either.
But I'm probably talking out of my ass. Don't worry about that stuff, dudes!
Edit: oh yeah, there are also specialized booze shops but I don't think they are open that late.