The clash in Basel, Switzerland, was tightly contested until the Polish team ultimately prevailed in the final minute, news outlets reported.
Poland right-back Monika Kobylińska said after the match: "It was really a tough game. It didn't work like we wanted. We started good and I don't know why we allowed them to come back. Portugal are playing a good handball and we are happy we managed to take two points."
Right-wing Magda Balsam said: "We're happy with the win, but our performance wasn't up to par. We need to do some soul-searching and move forward."
The victory keeps the Polish team's hopes of advancing to the main round alive, but they must defeat Spain on Monday to progress, Poland's PAP news agency reported.
Poland, coached by Norwegian Arne Senstad, suffered a 22-35 defeat to France in their opening match of the tournament.
The championship, co-hosted by Switzerland, Austria and Hungary, runs until December 15.
(gs)
Source: IAR, PAP, polskieradio24.pl, ehfeuro.eurohandball.com