It gives GB two wins from three matches and puts them within touching distance of securing their place in Division 1A for another year.
For the third match running, GB took an early lead, this time Brett Perlini the man responsible at 3.02.
Poland equalised through Pawel Dronia at 12.21, but they found themselves trailing before the end of the first after Colin Shields struck on the power play at 18.37.
A difficult second period saw GB cede the advantage to their rivals, who went into the second break 3-2 ahead after strikes from Damian Kapica and Krzysztof Zapala.
But two third period goals in as many minutes, first from Brendan Brookes and then Sheffield Steelers' Ben O'Connor gave GB a lead they never relinquished, captain Jonathan Phillips adding a last-minute empty net strike to ensure three points.
"This was another brilliant performance from the guys," said Russell. "Sure, we did not have it all our own way and we were a bit sloppy in the second period.
"But they came back so hard and found a way to get that win. I am so proud of this squad once again."