Edson Alvarez's close-range header set up a 2-0 victory on Wednesday at Johan Cruijff Arena and captain Dusan Tadic made sure with a fine goal 10 minutes from full-time.
Klaas-Jan Huntelaar had a goal ruled out for offside after a VAR check at 1-0, while moments later Andrija Pavlovic was denied an equaliser by the assistant's flag at the other end.
Ajax, semi-finalist last season under Erik ten Hag, knocked out PAOK to reach the play-off round and the Eredivisie champion will learn its fate in Friday's (AEST) group stage draw.
Slavia Prague is also in the hat after a second 1-0 victory in their tie against Cluj, Jan Boril scoring a second-half winner for the Czech champion.
Club Brugge completes the line-up after qualifying via a 3-1 aggregate win over Austrian side LASK, which had captain Gernot Trauner sent off in a 2-1 loss on Thursday (AEST).
Goals from Hans Vanaken and Emmanuel Bonaventure Dennis either side of a Klauss penalty sent the Belgian team through.