Stosur defeated Victoria Kan 6-2, 6-3 in 60 minutes in the first match Sunday to close out Russia in the best-of-five series. The Australians will Germany in the Fed Cup semifinals in April.
It is the first time since 1993 that Australia made the Fed Cup semifinals. That was also the last time the Australians played in the final, losing to Spain. The most recent of Australia's seven Fed Cup titles came in 1974.
Stosur had beaten Veronika Kudermetova and Casey Dellacqua topped Irina Khromacheva in Saturday's singles to a 2-0 Australian lead. Both of those matches lasted just less than an hour and Stosur needed only a couple minutes more Sunday to dispatch Kan.
She didn't face a break point while winning 32-of-38 points (84 percent) of the points on serve. Stosur also won more than half the points when Kan served and finished with four breaks.
The fourth singles match was called off and Dellacqua and Ashleigh Barty completed a 4-0 Australian sweep with a 6-1, 6-3 doubles win over Khromacheva and Valeria Solovyeva.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys