2022 champions Finland looked to have a second straight trip to the gold medal game within reach before Canada wiped out their two-goal lead at PalaItalia on Friday.
A day later, they had to return to the same ice to avoid leaving Milan empty-handed against a Slovakia team that had outperformed early expectations before losing to the USA.
"It was probably the biggest challenge of my life to get over that game. It was hard," said Finland forward Erik Haula, who scored two goals in Saturday's win.
"Talking to the other guys, talking as a team about what a medal means and stuff like that, that powered us through I think."
The medal may not have been the colour they had in mind but was nonetheless a fine conclusion to a tournament that got off to a rocky start.
Finland lost their preliminary stage opener to Slovakia, hardly the kickoff they wanted for their title defence, and were forced to regroup before beating Nordic rivals Sweden in their second game.
"First game, we kind of learned our lesson," said Joel Armia, who contributed a third-period empty netter in Saturday's rout. "We didn't just sit back and we had the courage to play with the puck and play confident."
Armia finished the tournament as Finland's top point-scoring, with eight, made up of three goals and five assists.