Sweden led 2-0 but could not withstand a strong Finnish onslaught.
With 24 seconds left, Roni Hirvonen rounded the Swedish box from the kitchen path and quickly wallowed in the puck.
Goalkeeper Hugo Alnefelt had left a small gap that Hirvonen found.
Finland had had two good positions in the same attack and the goal hung in the air.
The Swedish players collapsed after the final signal and stared with blank stares.
This is the final game for the Junior Crowns in the tournament in Edmonton, which began on 25 December.
This is the second time that Sweden went out before the semifinals.