Janne Pesonen collected a goal and an assist, while 'keeper Petri Vehanen produced 32 saves to grab the second world title for Finland.
"We proved that we're strong and menthally tough team," said Finland forward Leo Komarov.
"After the Swedes scored we didn't panic, we were working hard and managed to come back with a five-goal streak in the third period.
"I think we won the championship deservedly. And I want to believe we will never need to wait for 16 more years for our next win."
The rivals were playing against each other for the fourth time in a world championship final.
Finland, who won their only previous world gold in 1995, beating the Swedes on their home ice, fell behind in the second period when Magnus Paajarvi broke the deadlock firing in from the left face-off circle at 27:40.
The Finns levelled on powerplay with just seven seconds before the break through Jarkko Immonen, who scored his ninth goal here to grab the lead in the goal scorers contest.
Petteri Nokelainen and Niko Kapanen gave Finland a comfortable 3-1 lead, one minute into the third period.
Pesonen, Mika Pyorala and Anti Pihlstrom added further goals late in the third to complete the victory, sending Finland supporters into a celebration of their team's first world title in 16 years.
"It's a very sad and disappointing day for me," Sweden's Patrik Berglund said. "We were in command, we were leading the score. I just don't understand what has happened. We completely lost control. It sucks to lose this way."
Earlier on Sunday the Czech Republic outscored Russia 7-4 in the highest-scoring bronze medal match in the history of the event.
It was the Czechs' fourth bronze medal at world championship level.
Roman Cervenka collected two goals and two assists, while goalie Ondrej Pavelec produced 39 saves to give the Czechs a 8-6 lead in their head-to-head meetings with Russia at the worlds.