Trailing 3-1, the Finns came out flying in the third, scoring three goals in a little over three minutes with Niklas Hagman sparking the rally and Olli Jokinen contributing two before Valtteri Filppula sealed the win scoring into an empty net as the seconds ticked away.
It marked the fourth time in five Olympics Finland have landed on the podium while Slovakia were denied their first ever medal in men's ice hockey.
"If someone would tell us before the tournament that we're going to win the bronze medal, I would say we would take it right away," said Finland's Teemu Selanne, who leaves the Games as the Olympics all-time leading scorer.
"Obviously gold was our dream but we had no tools to be in the final. I think the two best teams are in the final and hopefully the better team wins tomorrow."
Canada will face off against the United States to decide the final gold medal to be handed out at the Vancouver Games on Sunday.
The surprise package of the ice hockey competition with upset wins over top ranked Russia and 2006 gold medallists Sweden, Slovakia had looked poised to end their Olympic adventure with one more shocker after jumping out to a 3-1 lead.
Sami Salo's power play accounted for all the first period scoring, the Vancouver Canucks defenceman stepping in over the blue line and blasting a slap shot past Jaroslav Halak to nose Finland in front.
But Slovakia hit back with a pair of powerplay strikes of their own in the second period from Marian Gaborik and Marian Hossa and added a shorthanded tally from Pavol Demitra to surge in front 3-1.
After Finland had taken the lead, Slovakia launched an all-out assault in the final minutes in a desperate bid to force overtime.
But they could not put another puck behind netminder Miikka Kiprusoff, who was solid in a bounce back performance after being shelled for four goals on seven shots in a 6-1 semi-final loss to the United States.
While Slovakia were crushed that they would not be returning home with a medal, the fourth place finish goes into the record books as the country's best ever Olympic result.
"We wanted a medal so badly," said Marian Hossa. "It's just a tough pill to swallow right now because we were in such a great position coming into the third and we got into penalty trouble.
"But I think we can be proud of our guys. We did a lot of good things but it's not what we wanted to finish fourth."
Three members of the Finnish team, Jere Lehtinen, Ville Peltonen, Saku Koivu all received their fourth Olympic medals doubling the membership of an exclusive hockey club that includes the Czech Republic's (formerly Czechoslovakia) Jiri Holik, Soviet Union's Vladislav Tretyak and Russia's Igor Kravchuk.