Shamrock Rovers remain without a point in Group A in the Europa League and now have no chance of making it through to the knockout stages.
Dimitris Salpingidis scored twice and Giorgos Fotakis got the other as PAOK Salonika took a 3-0 half-time lead.
Billy Dennehy pulled one back in the 51st minute for Rovers who recently retained the League of Ireland title.
The Greek side are now top of the group following Tottenham's 1-0 defeat by FC Rubin Kazan in Russia.
Salpingidis made the early breakthrough when Adelino Vieirinha's pass put him clean through and the striker placed his shot past the advancing Ryan Thompson.
It was a weak strike and the ball trickled in to the back of the net before Shamrock defender Craig Sives could make a clearance.
PAOK got their second in the 35th minute after Salpingidis intercepted a pass and played in Fotakis who fired in.
Salpingidis netted the Greek side's third three minutes later from close range after he got on to the end of Georgios Georgiadis's accurate delivery from the right.
Dennehy scored six minutes into the second half when his 25-yard free-kick flew past PAOK goalkeeper Kostas Chalkias.
Adelino Vieirinha then hit the post and later saw his shot fly over the bar as the Athens side searched in vain for their fourth goal.
However, it was still a comfortable win for the Greek side which puts them one step closer to the knockout stages.