An incisive performance from Francesco Guidolin's men saw them go two goals up within 15 minutes, leaving the Greek outfit floundering throughout the encounter.
Danilo gave the visitors the lead after a matter of minutes, before Antonio Floro Flores doubled his side's advantage. Mauizio Domizzi added a third from the spot just after halftime to give his side a handsome victory.
The first leg of this encounter had finished goalless at Stadio Friuli, but from the outset, it was obvious that both sides were intent on opening the scoring early.
Kwadwo Asamoah fired wide within a minute of kick off, before a defensive lapse allowed Dimitris Salpingidis a shot on goal, but one that was quickly snuffed out by the Udinese backline.
Apostolos Giannou forced a credible save from Samir Handanovic before the deadlock was finally broken by the visitors.
Giovanni Pasquale put a corner in from the left, and Danilo was there to nod the ball past a flat-footed Dario Kresic.
The onus was now on the hosts to attack, but on the quarter-hour mark, Udinese extended their lead. Domizzi slid the ball to Floro Flores, who smashed into the top corner from 25 yards.
Despite the volley of away goals leaving the Greeks in dire straights, they continued to pepper the Udinese goal. Pablo Garcia swung in a corner that Bruno Cirillo sent onto the post, before another of the Urguayan's deliveries was nodded over by Stelios Malezas.
Stefanos Athanasiadis screwed a right-footed shot narrowly wide of the target with the break approaching, before Giannou sent a lovely effort from the edge of the area inches off target.
In the end, they were unable to produce a goal that would give them a way back into the tie before the break.
PAOK came out after the interval with renewed vigor, but moments into second period, the club was dealt a killer blow.
Miroslaw Sznaucner tugged back Floro Flores as the Italian looked to get past the Polish defender. The referee pointed to the spot and Domizzi made no mistake, putting his side into a 3-0 lead.
The third goal deflated the hosts. Diego Fabbrini forced a great save from Kresic, with Floro Flores sending the rebound into the side-netting from a tight angle.
The Greeks rallied in search of a consolation goal, and had muted appeals for a penalty of their own ignored by the officials, before Salpingidis forced a save from Handanovic from the edge of the area.
They remained vulnerable at the back as they poured bodies forward, though, with Cristian Battocchio fired wide from 18 yards after some cunning work from Floro Flores down the left.
There was to be no reward for PAOK's brave efforts, while three goals was more than enough for the Serie A outfit to set up a tie with AZ or Anderlecht.