Nicolas Gaitan, Rodrigo Lima and Lazar Markovic struck in the last 20 minutes on Thursday night after the dismissal of former Benfica player Konstantinos Katsouranis allowed the Portuguese side to take control.
Katsouranis had received a good reception at the Estadio da Luz but was sent off for denying Lima a goalscoring opportunity.
The final scoreline flattered Benfica, who will now play Tottenham in the next round, but there was no denying their superiority.
The hosts did have a scare early on when Artur almost let a Sekou Oliseh shot squirm in. The goalkeeper failed to hold onto the low drive but scrambled back and dived on the ball on the line.
That sparked Benfica into action and PAOK goalkeeper Panagiotis Glykos saved from an Eduardo Salvio strike and a deflected Oscar Cardozo free-kick.
Gaitan also dragged a good opportunity wide and Cardozo was narrowly off target with another fine effort.
Benfica remained untroubled in the early stages of the second half but their efforts to break through were laboured.
Ezequiel Garay and Filip Djuricic did have shots blocked by Katsouranis and Stelios Kitsiou respectively, but it was not until the the sending-off of their former midfielder that Benfica finally took control.
The PAOK captain was caught out as Lima raced onto an Andre Gomes ball and brought him down.
Gaitan made the Greeks pay the price as he clipped a fine free-kick over the wall and in at the near post.
PAOK then capitulated as two more goals followed in quick succession.
Hedwiges Maduro was caught out by a high bounce as the ball struck his hand.
Lima made no mistake from the penalty spot and substitute Markovic completed the job 10 minutes from time after Luisao won possession and released him with a long ball.