Having trained in the same group in Odessa, Grushina and Ruslan Goncharov were paired together in 1989. They finished fourth at the 1992 Junior Worlds. They were 18th in their senior Worlds debut at the 1994 World Championships. In early 1997, Grushina and Goncharov began training with coaches Natalia Linichuk and Gennadi Karponosov in Newark, Delaware. They finished 15th at their first Olympics in 1998. They won their first Grand Prix medal, silver, at 1999 Skate Canada International.