A visibly tired PAOK, having played in Israel in the Europa League on Thursday, could only contain the Reds in the first half-hour.
Campbell took over after that, setting up Super League top scorer Kostas Mitroglou for his 14th goal of the season in the 36th and then combining with Argentine Javier Saviola who made it 2-0 on the hour mark.
Spaniard David Fuster made it 3-0 in the 74th before Campbell, in his best game for OIympiakos since joining in July, scored the fourth 10 minutes from time.
Olympiakos have 31 points from 11 games, while PAOK stayed at 25, seven more than third-placed Atromitos.
- Sports & Recreation
- Kostas Mitroglou
- Javier Saviola