Scotland won gold with a 6-2 win over Russia.
Canada blanked the first end and then scored three points in the second.
After blanking the third end, the Swedes responded with two points in the fourth end, but after that the teams swapped singles all the way to the ninth end, when, with the score at 5-4 in their favour, Canada blanked again.
In the tenth end, Canada's third player, Colton Lott, played a good double take-out that cleared out Swedish stones in the house and laid the foundation for another point.
Dunstone's Winnipeg rink was the youngest at the tournament.
"Age doesn't matter," the 17-year-old skip said after the match. "We just go out and play our best. Obviously whenever you finish a tournament off with a win it's a very good thing. We're going home with a medal for Canada and that's an unbelievable feeling."
Russia was making its first appearance in a junior world final after beating Canada 11-8 in an extra end in Saturday's semifinal. But they were no match for Scotland's Kyle Smith, who led his team with steals in the fourth, fifth and seventh ends.
In women's action, Russia won gold with a 6-5 extra-end win over Scotland. Japan took bronze with an 8-4 rout of the Czech Republic.