Having set up Therese Sjogran for the opening goal in the 11th minute, Schelin made the match safe in the 52nd to set off the players' traditional Swedish dancing celebrations.
Schelin capitalized on a poor back pass from Kim Carroll, took one touch past goalkeeper Melissa Barbieri before slotting the ball into the unguarded net.
"There is a fantastic atmosphere in our team and we pulled each other through," said Schelin, the player of the game.
The result means Sweden also qualifies for the London Olympics next year.
"Now we have to concentrate on winning against Japan. We don't have very good memories of playing against them," Sweden coach Thomas Dennerby said. "Our players will work hard to go one step further."
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