PAOK were adjudged to have broken the Greek football federation (EPO)'s ownership rules by having a stake in league rivals Xanthi FC.
The court upheld PAOK's appeal and referred the case back to the EPO, who must deliver a fresh verdict.
The temporary decision restores PAOK to second place in the Greek top division behind newly-crowned champions Olympiakos, with three rounds to play.
Olympiakos are guaranteed a spot in the third qualifying round of the Champions League, while the runners-up enter the second qualifying round of the Europe's elite competition.
"The CAS panel found that, notwithstanding its power to decide the case itself, it was not appropriate to render a final and binding decision in such circumstances, with major consequences for Greek football," the court said.
Olympiakos had also lodged a complaint against the EPO's decision, asking for harsher sanctions to be imposed on PAOK and Xanthi.
The court also confirmed Xanthi's seven-point deduction remains in place as they did not appeal against it. (Reporting by Hardik Vyas in Bengaluru, editing by Pritha Sarkar)