At the age of fifteen, in 1982, Baginskate became second at women's chess championship of the Lithuanian Soviet Socialist Republic, behind Esther Epstein.
In 1986, she was third after Ildikó Mádl and Svetlana Prudnikova at the World Junior Girls Championship in Vilnius, her home city.
Baginskaite studied design in Lithuania and the US with a master's degree in history of art.
For many years, Baginskaite played on the first board for Lithuania at the Women's Chess Olympiad in 1994 and 1996.
Since Baginskaite won against Groberman in the playoff by 2-0, she qualified for the Women's World Chess Championship 2001 in Moscow, where she reached the last sixteen.