Needing all three points to leapfrog this summer's World Cup hosts a clinch victory in their group, Olsen was a wall at the back - as Victor Lindelof and Marcus Berg scored either side of half-time to confirm the victory.
Elsewhere on Tuesday night, Aleksandar Kolarov was an unused substitute as Serbia clinched their own promotion with an emphatic 4-1 win over Lithuania.
Steven Nzonzi was a late introduction in France's 1-0 win over Uruguay - as Olivier Giroud scored the only goal of the game.
Finally, Cengiz Under played all 90 minutes in Turkey's 0-0 draw with Ukraine.
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