It was just the second world women's championship medal for Russia after winning bronze in 2001.
Shibanova scored a power-play goal at 4:11 of the third period. Alexandra Vafina added an empty-net goal with 15 seconds remaining.
Russia's goaltender Nadezhda Alexandrova made 32 saves for the shutout
Finland's Noora Raty, an NCCA star with the Minnesota Golden Gophers, stopped 15 of 16 shots.
Canada faced the United States for gold later.