The home side had plenty of the ball in the early stages of the half as Shinji Kagawa and Pascal Stenzel had early shooting opportunities, while Adnan Januzaj and Park Joo-hoo delivered some decent crosses into the box.
All the attacking play came from Dortmund as Stenzel attempted another shot from just outside of the penalty area, but the ball was blocked by PAOK's defence.
Adnan Januzaj, who has struggled to hold down a first-team spot, tried to prove himself by getting involved on the flanks, but he took some time to find his rhythm.
The home side should have been a goal to the good in the 23rd minute when Matthias Ginter received the ball in the six-yard box, but his shot flew over the crossbar.
A few minutes later against the run of play, PAOK had the ball in the back of the net thanks to Georgios Tzavellas, but it was disallowed as Robert Mak was offside when he headed the ball on.
Not long after, though, PAOK did edge in front when Dimitrios Konstantinidis delivered a decent pass to Mak, who slotted home from close range in the middle of the box.
Both Januzaj and Marco Reus had chances to bounce back after going a goal down, but both failed to make it count before the half-time whistle.
Januzaj will be lucky to return to the pitch for the second half as he was let off with just a booking following an elbow shove that was worthy of a red.