Cheryshev, who plays for Spanish side Villarreal, scored four goals in five matches to equal Portugal striker Cristiano Ronaldo's haul at the tournament while Zenit St. Petersburg striker Dzyuba chalked up three goals and two assists for the host nation.
Both 27-year-old Cheryshev and Dzyuba, who is 29, were playing at the World Cup for the first time.
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The US TV channel ESPN also named the likes of South Korea goalkeeper Cho Hyun-woo, France defender Benjamin Pavard and Japan midfielder Takashi Inui in their 11-man World Cup squad of breakout stars.
Russia were eliminated from this summer's tournament after losing on penalties to Croatia in the quarter-finals on Saturday.
The 2018 FIFA World Cup kicked off on June 14 and will continue until July 15, with the final set to be held at Moscow's Luzhniki Stadium.