Serbia winger Andrija Zivkovic scored against his former club Benfica a week after leaving them.
Dynamo Kiev also advanced to the play-off round with a 2-0 home win over Dutch side AZ Alkmaar, as did Belgians Gent after they beat visitors Rapid Vienna 2-1.
PAOK’S reward is a two-legged play-off against Russians Krasnodar, while Dynamo Kiev face Gent for berths in the money-spinning group stage featuring 32 teams.
Benfica, who won Europe’s premier club competition in 1961 and 1962, saw last season’s woes spill over into this term.
This was as Zivkovic, who endured four difficult seasons in Portugal, rubbed salt into their wounds.
Having seen the domestic league and Cup double go to Porto last term, Benfica missed a string of chances against PAOK in a one-sided first half as they enjoyed 72 percent of possession.
They were punished after the break as Dimitrios Giannoulis poked in the opener from close range in the 63rd minute.
That was after a one-two with Chuba Akpom, and substitute Zivkovic made it 2-0 in the 75th with a sweet shot inside the near post.
Rafa Silva pulled one back with a stoppage time header but it came too late to avoid an embarrassing defeat.
This will pile pressure on manager Jorge Jesus, who returned to Benfica during the close season for a second spell in charge.
Having been in charge from 2009 to 2015, Jesus went on to win the elusive double of the Brazilian league title and Copa Libertadores with Flamengo in 2019.
But he now faces a mammoth task to get Benfica back to winning ways.
Dynamo Kiev soaked up pressure on home soil against Alkmaar in the first half.
Then, Luxembourg forward Gerson Rodrigues fired them ahead just after the break with a neat finish into the roof of the net, thanks to good work by Vitaliy Buyalskiy.
Mykola Shaparenko sealed their passage with a late header after visiting goalkeeper Marco Bizot misjudged Tomasz Kedziora’s cross from the right.
It left the midfielder with the simple task of nodding the ball into an empty net.
Niklas Dorsch headed Gent into a 36th minute lead against Rapid Vienna from a pinpoint Sven Kums assist.
Roman Yaremchuk added the second with a penalty kick on the hour, before Yusuf Demir netted a stoppage time consolation for the visitors.
In Wednesday’s stand-out fixtures, 1991 European Cup winners Red Star Belgrade visit Cypriots Omonia Nicosia while Dinamo Zagreb are at Hungarian champions Ferencvaros.