The Frenchman netted twice in the space of 10 minutes following Yevhen Khacheridi's early sending-off for the visitors.
Giroud was joined on the scoresheet by youngster Callum Hudson-Odoi, who got off the mark with his first goal for the club on the hour, before setting up substitute Alvaro Morata for his side's fourth of the night.
Brought back into the side as one of 10 changes from the 3-1 loss to Chelsea last weekend, Giroud made an immediate impact as he pounced on a stray pass and charged through on goal.
Khacheridi was forced to hack down the former Arsenal striker and was shown a red card by Kristo Tohver inside the opening seven minutes, making a tough task for PAOK all the more difficult.
Chelsea were having no problems turning possession into chances, as Giroud and Pedro both came close to netting with their efforts, while Hudson-Odoi also tested Alexandros Paschalakis on his first start since August.
The visiting keeper would also be needed to push aside a powerful drive from Ruben Loftus-Cheek, who netted a hat-trick against BATE in Chelsea's most recent European outing here, but the breakthrough arrived before the half-hour mark.
Pedro slotted a pass through for Giroud, who tucked the ball out of Paschalakis's reach with a smart finish to make it three goals in three games.
That record was extended soon after as Giroud this time volleyed Cesc Fabregas's chipped pass past Paschalakis at the Greek keeper's near post.
Hudson-Odoi curled a shot against the crossbar between those two goals and Pedro had a couple of shots kept out in a dominant first-half showing from the hosts.
Another good stop from Paschalakis to thwart Loftus-Cheek kept the scoring down until the hour, at which point Hudson-Odoi got the goal he craved by working the ball onto his right boot and passing it into the bottom corner from 12 yards.
Chelsea's next big chance led to the fourth goal of the contest, as Morata got between two opposition men to guide Hudson-Odoi's right-sided cross into the back of the net just three minutes after being brought off the bench.
Another second-half sub in Willian should have added to Chelsea's tally late on, only to meet his match in Paschalakis, and Barkley clipped the roof of the net from his free kick in the final minute of play as Sarri's men returned to winning ways with ease.
CHELSEA (4-3-3): Kepa; Zappacosta (Ampadu 63'), Christensen, Cahill, Emerson; Barkley, Fabregas, Loftus-Cheek; Pedro (Willian 66'), Giroud (Morata 75'), Hudson-Odoi
PAOK (4-2-3-1): Paschalakis; Matos, Khacheridi, Crespo, Vieirinha; Mauricio (Pelkas 79'), Wernbloom; Jaba, Shakhov, El Kaddouri (Varela 75'); Prijovic (Warda 46')