The away side opened the scoring in the 10th minute through a free-kick from Moroccan international Hakim Ziyech.
However, the hosts restored parity in the 32nd minute after Dimitris Giannoulis’ cross from the left flank found an unmarked Chuba Akpom in the box, allowing the Nigerian forward to finish with aplomb.
The Greek side then took the lead for the first time in the game through Leo Matos’ effort in the 39th minute.
The second-half saw the Dutch club mount pressure on the home side in search of an equalizer, and it duly came in the 57th minute through Klaas Jan Huntelaar.
Chuba Akpom, Anderson Etiti and Moroccan international Omar El Kaddouri played the entire duration of the game for PAOK, as did Andre Onana in goal for Ajax, while Ziyech was substituted in the 82nd minute for David Neres.
The African stars will hope to continue their impressive form when both sides meet on August 13 for the reverse fixture at the Johan Cryuff Arena.