A powerful drive by Russia defender Georgy Dzhikiya after a corner hit the post found Neustadter, who tapped the ball past Turkey goalkeeper Sinan Bolat to open scoring in the 20th minute.
Russia doubled their lead in the 78th minute when substitute Cheryshev latched on to Aleksandr Golovin's cross and fired home with a left-footed shot just inside the near post.
Russia, surprise quarter-finalists at this year's FIFA World Cup, lead Group 2 with seven points. They will travel to Sweden, who are bottom of the standings with one point but with a game in hand, on November 20. Turkey have three points.