I’m not aware of any Portuguese word specifically for ‘party with a lot of drinking going on’. If a phrase will do, you could use festa bem regada:
Fomos a um aniversário na casa do Peter, mas depois à noitinha aquilo deu numa festa verdadeiramente bem regada
Regar (Aulete) literally means ‘to water’ (plants), but it’s used informally to mean ‘to have drinks with’ (a meal, a party). Here are some examples of actual usage (my emphasis in all quotes):
“Esta tem sido uma festa bem regada”, confessa-nos um dos elementos. As garrafas, numa contagem rápida, aproximam-se da meia centena. Mas duas grades ainda estão intactas.
[«A volta no seu esplendor», Correio da Manhã (Portugal), 2005]
Norte Americanos […] deixaram roubar um computador com programação secreta depois de uma festa "bem regada" na companhia de prostitutas.
[Agência Angola Press, 2002]
There are a couple of single words that by themselves won’t imply a party, but in the right context, as in your sentence, may convey the right meaning:
Fomos a um aniversário na casa do Peter, mas depois à noitinha aquilo deu numa verdadeira borracheira
Borracheira (Aulete) is an informal word for an action, talk, or state of a drunken person, from borracho (Aulete), ‘drunken’. So the emphasis here is on getting drunk, and someone hearing the sentence above might get the impression that things went a little down the hill, where propriety is concerned, at the party. You could off course use bebedeira (Aulete) instead. But while bebedeira simply means the ‘state of being drunk’, borracheira is broader, including silly things you do while drunk. Here’s from an advert for the “Borracheira da Engenharia”, a student party at Universidade Federal de Santa Maria (Rio Grande do Sul, Brazil):
A festa contará com decoração diferenciada da Ensaio Formaturas, venda de vodka com energético e novas surpresas! Não perca!
“VEM PRA BORRACHEIRA VOCÊ TAMBÉÉM... VEM!!”

For a milder tone you could go for:
Fomos a um aniversário na casa do Peter, mas depois à noitinha aquilo deu numa verdadeira copofonia
Copofonia (Priberam) (seemingly not used in this sense in Brazil) is an informal word for the loud noise of people drinking or the drinking itself. It comes from copo (Aulete 5), ‘drinking glass,’ and a rather common metonym for alcoholic drink. So this version of the sentence puts more emphasis on drinking and lots of noise and activity, rather than getting drunk. It looks as though this word is not used in Brazil, but it has a long tradition in Portugal. There even has been an “Associação Técnica de Copofonia”, as attested by this membership card I found in blog Pombalinho:
