A quick-fire brace from Hassan had Alan Pardew's side on the back foot, and a third goal was added for the hosts by Braga.
The Magpies improved after the interval, but had only a solitary strike from Shola Ameobi to show for their efforts.
It took just six minutes for Rio Ave to break the deadlock, as Hassan hooked home past the despairing dive of Jak Alnwick.
He went on to double his tally three minutes later, before Braga made it three on 26 minutes - sweeping in from eight yards out following good work by Del Valle.
Pardew rang the changes at half-time and one of those introduced, Ameobi, reduced Newcastle's arrears when he converted from a Gabriel Obertan cross.
Rio Ave could have made the scoreline even more comprehensive five minutes from time, but Lima saw a penalty he won after being bundled over by Mike Williamson saved by Rob Elliot.