Last season’s semi-finalists Ajax, who have won Europe’s premier club competition four times, made a perfect start in the cauldron of PAOK’s Tumba stadium.
Hakim Ziyech curled in a swerving free kick after 10 minutes.
Roared on by a fervent home crowd, PAOK turned the tide before half-time.
Striker Chuba Akpom capped a flowing move with a fine finish from 10 metres and defender Leo Matos headed home a Diego Biseswar free-kick.
Ajax, who suffered a last-gasp defeat by Tottenham Hotspur in last season’s semi-finals, piled on the pressure after the break.
Ziyech missed a glaring chance before substitute Klaas Jan Huntelaar equalised with a bizarre goal on the hour.
Fernando Varela’s poor clearance from Donny van de Beek’s cross rebounded off the 35-year old striker’s feet into the back of the net from close range.
The visitors then dominated until the final whistle.
In other matches also played on Tuesday, Red Star Belgrade could only manage a 1-1 home draw against FC Copenhagen.
Azeri champions Qarabag took a big step towards the playoff round with a 2-1 win at Cypriot side APOEL.
But Dinamo Zagreb left their progress hanging in the balance after the Croats played out a 1-1 home draw against Hungary’s Ferencvaros.
A Hans Vaneken penalty kick late in the first half gave Bruges a 1-0 home win against Dynamo Kiev.
Red Star, the 1991 champions, conceded a late equaliser after their striker Milan Pavkov reaffirmed his reputation for scoring in big games just before the break.
But he had to be forced off the pitch at half-time by a recurring hamstring injury.
Pavkov, who netted twice in last season’s memorable 2-0 home win over eventual UEFA Champions League winners Liverpool in the group stage, fired Red Star ahead in the 44th minute.
That was when he hooked a loose ball over goalkeeper Sten Michael Grytebust.
Pavkov made way for Richmond Boakye and the hosts were punished in the closing stages for the Ghanaian’s forward’s second-half profligacy.
Boakye missed a pair of gilt-edged chances to double Red Star’s lead before midfielder Dusan Jovancic fouled Copenhagen substitute Mas Jaume in the penalty area.
Jonas Wind coolly converted the 84th minute penalty kick.
Dinamo’s Spanish midfielder Dani Olmo fired them ahead with a superb goal in the seventh minute as he took a clever back-heel by Mislav Orsic in his stride.
He then nutmegged a defender and hit the far corner of the net with a crisp shot.
But Ferencvaros levelled against the run of play on the hour when David Siger beat Dominik Livakovic with a looping header after the goalkeeper had parried a shot from 10 metres.
Goals from Mair Emreli and Magaye Gueye gave Qarabag a 2-0 lead at APOEL before Giorgos Merkis pulled one back for the home sides in the 90th minute.
In Wednesday’s stand-out fixtures, 1967 European Cup winners Celtic visit Romania’s CFR Cluj while twice former champions FC Porto are away to Russians Krasnodar.