Linda Klimovicova opened the tie with a 6-2, 6-1 win over Elena Ruxandra Bertea.
Iga Świątek followed with a dominant 6-2, 6-0 victory against Gabriela Lee, earning her 14th singles win in BJK Cup play.
Doubles players Katarzyna Kawa and Martyna Kubka sealed the sweep with a 6-2, 6-3 win in the final match.
Both Poland and Romania had earlier beaten New Zealand 3-0, making their head-to-head meeting the decider for the top spot in Gorzów Wielkopolski.
Klimovicova, born in the Czech Republic and ranked No. 146, received Polish citizenship last year.
She earned her spot in the singles lineup after a strong doubles performance on the opening day.
"I’m very happy to win a point for Poland. Thank you to the fans for the support—you’re wonderful," she said.
Świątek said playing at home made the matches special.
"I play many matches during the year, but these two in front of our home crowd were exceptional," she said.
"The team atmosphere is amazing. I’d love to play more matches with Team Poland," she added.
With Sunday's win, Poland moved on to the final stage of qualifying scheduled for April.
Last year, Poland, led by Świątek, reached the Billie Jean King Cup semifinals for the first time, narrowly losing to eventual champions Italy.
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Source: IAR, PAP
Click on the audio player above for a report by Marcin Matuszewski.