Chelsea showed little nerves in the hostile atmosphere at the Toumba Stadium from the opening whistle, and it took the Blues less than seven minutes to go ahead.
Chelsea continued to look for goals and Alvaro Morata should have doubled his side's lead within three minutes, only to head wide of the near post after meeting Pedro's cross.
The forward then drilled a low effort from an acute angle marginally wide of the far post, while Andreas Christensen should have done better at the back post after meeting a corner.
Pedro was the next player to squander an opening after the half-hour mark with the winger latching onto a superb through-ball from Marcos Alonso, but Paschalakis remained big to prevent the Spaniard from finding the far corner.
Chelsea continued to control the pace of the game after the restart and a second goal should have arrived in the 49th minute when Pedro and Barkley combined to tee up Willian, but the playmaker's shot was poor and too close to Paschalakis.
Willian was guilty again just before the hour mark, with a volley being sliced over the crossbar from 12 yards after good work from Pedro on the right.
Alonso was getting forward with regularity, and in the 61st minute the left-back cut back onto his weaker right foot before seeing a shot deflected marginally wide of the post.
PAOK were offering nothing in the final third, but Chelsea's frustrations continued at the other end as Pedro was superbly denied with an acrobatic save from Paschalakis when his shot appeared destined for the top corner.
Diego Biseswar was introduced by the home side as the game entered the closing 10 minutes, and the Dutchman soon warmed the hands of Kepa Arrizabalaga with a well-struck shot from inside of the penalty area.
Chelsea went back up the other end and threatened through substitute Olivier Giroud, who saw a low effort tipped wide by Paschalakis, but the West Londoners were happy to make do with the solitary goal as they began their Europa League campaign in style.
However, in added-on time, Pedro collided with Paschalakis after being fouled outside the box, and the Spaniard could be set for a few weeks on the sidelines with an arm injury.
PAOK (4-3-3): Paschalakis; Vierinha, Khacheridi, Varela, Tosca; Mauricio, Shakhov (Prijovic 69'), Wernbloom; Jaba (Biseswar 82'), El Kaddouri, Pelkas (Warda 62')
CHELSEA (4-3-3): Arrizabalaga; Zappacosta, Christensen, Rudiger, Alonso (Azpilicueta 66'); Jorginho (Fabregas 65'), Kante, Barkley; Willian, Pedro, Morata (Morata 81')