The Russians came into this second leg with a one-goal advantage but they almost threw it away with a poor start, Vladimir Ivic firing wide.
Bruno Cirillo volleyed wide before Zlatan Muslimovic struck the post, and the latter produced a weak finish that failed to trouble home goalkeeper Igor Akinfeev after the break.
PAOK finally took a deserved lead just after the hour mark, albeit in bizarre fashion, when Moscow’s substitute goalkeeper Sergei Chepchugov attempted to clear the ball and it struck the on-rushing Muslimovic and flew into the net.
Dimitris Sapigidis should have secured the visitors’ progress but he failed to connect with Ivic’s pass, and they were punished when Sergei Ignashevich stroked home the rebound after Vagner Love’s penalty had been parried by Dario Kresic.