The five-time Olympian hit a slap shot that bounced off the ice and hopped over Swiss Andrea Braendli's pad to make it 1-0 for the Canadians in the second period at Santagiulia arena, breaking compatriot Hayley Wickenheiser's record.
Poulin flipped in another score less than seven minutes later as she was diving towards the net.
The future Hall of Famer missed Canada's final two group-stage games with a knee injury in Milan but returned for Canada's 5-1 quarter-final win over Germany on Saturday, where she tied the record with her first goal at Milano Cortina.
Defending champions Canada are seeking a sixth Olympic gold.