Denis Cheryshev came close to giving the hosts an early breakthrough, but his well-struck left-foot drive ended narrowly wide of the target.
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Russia upped the pressure as the first half advanced, winning a succession of corners which they failed to make the most of with their opponents remaining solid.
The side ranked 105th in the world managed to hold on until the break, though, to set up a potential upset at the Otkrytie Arena.
Glushakov blew a glorious chance to fire Fabio Capello's men ahead 10 minutes after the restart when he blazed his shot over the bar after latching onto a rebound, while Artem Dzyuba glanced his header wide moments later.
The breakthrough did finally come after 73 minutes, however, when Viktor Golovatenko brought down an opposition player inside the area, allowing Dzyuba to step up and convert from the spot.