The New Zealand women were sitting on just one point after an overtime loss to South Korea earlier in the week, but a South Korean victory over Australia earlier on Sunday gave the Ice Ferns a chance of staying up and relegating their transtasman rival.
And so it proved, as the Ice Ferns overcame a 2-1 deficit going into the final period to score three times and claim the victory.
Krystie Woodyears-Smith drew the Ice Ferns level before Anjali Thakker put New Zealand ahead 3-2 with seven minutes remaining.
Thakker again came to the rescue after Poland equalised 90 seconds later, taking advantage of a power play to score the winning goal with 2 minutes remaining.
Meanwhile, the New Zealand men's team finished its world championship event in the Spanish city of Jaca in third position in the six-team division 2, group B competition after a 6-2 loss to Spain on Sunday.
Despite the last-day loss, the Ice Blacks had plenty to be proud of with wins over Turkey, South Africa and China during their five games.
Dunedin Thunder players Luke Pickering and Mitchell Frear scored goals in the tournament, Frear scoring one in the loss to Spain, while Thunder defenceman Regan Wilson won the team's hardest worker award.
Southern Stampede forward Callum Burns also recorded a goal, as did defenceman Berton Haines.
