Finland, ranked No. 3 in the world, fell out of medal contention four years after winning the bronze.
Florence Schelling made 41 saves in the second quarterfinal contest to bring Switzerland a 2-0 decision over Russia.
Sweden thus earned a meeting with the United States and Switzerland will face Canada Monday in the semifinals. Canada defeated Switzerland 5-0 in group play.
The Finns took a 1-0 lead into the third period, but Anna Borgqvist and Lina Webster scored in the opening 5:09 of the final stanza to put Sweden in front.
After Finland tied the score on a goal from Emma Nuutinen, Eliasson struck back to put Sweden in front for good. Emma Nordin scored into an empty net in the final minute.
Valentina Wallner made 29 saves to get the victory.
Schelling withstood a Russian barrage in the second game and Switzerland broke through midway through the first period on a goal by Steafnie Marty. It remained a 1-0 contest until Lara Stadler scored an empty-net goal with 21 seconds remaining.