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.
Pavlyuchenko had given Russia the lead in the 24th after being set up inside the box by Aleksandr Anyukov following a series of quick passes that ripped open the defense.
For their part, the Glasgow outfit were limiting Zenit to long range efforts and an Anatoly Tymoschuk drive and an Alexander Anyukov half-volley were easily dealt with by goalkeeper Neil Alexander.