Chris Finch's side had lost their last three matches, although they were against sides ranked second, fifth and sixth in the world, compared to their position outside the top 50.
It meant they had to brush aside Portugal to stand any chance of progressing to the next phase - and they did in style.
Chicago Bulls star Luol Deng again top scored with a mammoth 31 points, 21 coming in a one-sided first half.
Mike Lenzly contributed 17 points in a stand-out show while veteran Nate Reinking scored nine as solid contributions were made across the roster.
"Id like to congratulate our guys for our first win at EuroBasket," said Finch, whose side now face Poland in their final group game on Monday, although their chances of progressing are slim.
"It was a small victory, but a meaningful one. Portugal are an emotional team, and we were concerned about them as they can really get going. Guarding the three point line was important, but offensively we were much better.
We moved the ball well, and Luol was the catalyst for that. Everyone will look at his 31 points, but he had four assists and when he played like that he is at his best.
"Having Robert Archibald back helped, and our younger guys also played well which we needed them to do."