As Russia continued to run rings around the Irish, the second goal came on 28 minutes as Alexander Anyukov's run and pull-back set up Dzagoev to score.
For their part, the Glasgow outfit were limiting Zenit to long range efforts and an Anatoly Tymoschuk drive and an AlexanderAnyukov half-volley were easily dealt with by goalkeeper Neil Alexander.
Rangers goalkeeper Neil Alexander was then called into action when Brahim Hemdani lost possession just outside the box and the ball broke to Aleksandr Anyukov whose smart shot was initially fumbled and then held by Alexander.