The Russians equalized with three minutes left of regular time and looked to the Olympic quarterfinals in the hockey tournament to extend.
Then Switzerland responded by putting 3-2 half a minute later before they wrote the final result to 4-2 in an empty cage.
Thus, Switzerland is ready for the semifinals.
The fourth and final quarter-final between Finland and Japan will be played later on Saturday.
Canada, which outclassed the Damkronorna by 11-0, and the USA are already ready for the semifinals.