The Eagles went into the contest as major underdogs, but a second-half volley from Bekim Balaj was enough for the visitors to claim all three points in Aveiro.
Speaking after the match, midfielder Cana told reporters: "It was a dream start, a perfect start for us. We had to start qualification away from home in Portugal, the group favourites, and I still think they are the group favourites.
"It was a historic result to win against a big team in Europe, so I am very happy for my country and for my people. They were all looking to the national team. This victory is for them and we will try to do the best that we can until the end of qualification."
Next up for Albania is a home clash against Denmark in October.