Recent signing Dimitar Berbatov started up front for the hosts, but it was Slovakian striker Robert Mak who gave PAOK a first-half lead.
Gonzalo Castro equalised in fortunate fashion 18 minutes from time, though. His clipped ball into the box was meant for Jonas Hofmann but it evaded him and goalkeeper Robin Olsen and crossed the line.
Dortmund top the group by a point from FC Krasnodar, who beat Qabala 2-1 in Russia.