Or Brazilian /'sedʒi/ is cognate with Spanish <sed> 'thirst'. A Spanish speaker will have to know to effectively ignore the /ʒi/ in order to recognize the word easily!
Maybe more extreme, Brazilian /'hedʒi/ (written <rede>) is cognate with Spanish <red> 'net, network'.
You might also be familiar with a greater variety of Spanish pronunciations as a non-native speaker... if you know Argentine /'ʃubja/ and /'ʃabe/, then you have a better chance to recognize Brazilian /'ʃuvɐ/ and /'ʃavi/ ('rain' and 'key', respectively).
I should have specified in my original post, but I only meant that Portugal Portuguese (and at least a few of the African varieties that are still very close to Portugal's) are mutually intelligible with Spanish. Which actually just further illustrates the complexity of categorizing speech into discrete languages...
I'll concede that it's possible that I actually have an advantage as a second-language speaker, since my Spanish is probably slower than a native's and when I'm listening I'm already doing more work than a native is accustomed to.