The first two rounds were scored evenly as neither fighter managed to consistently land their shots.
Most of the fight was fought on the inside. Volnova edged in front after the third round thanks to the volume of punches she got off.
Marshall started the final round at a furious pace, landing a few fierce shots as she battled to keep her hopes intact.
However, the Kazakh boxed cleverly to score a 16-12 decision.