The Dutch side beat Dynamo Kiev 3-1 at home, while AEK triumphed 2-1 at Videoton in a game that saw both sides reduced to 10 men.
Donny van de Beek gave Ajax the lead after just 74 seconds at the Johan Cruyff Arena, his tame shot somehow squirming through the grasp of goalkeeper Denys Boyko.
Dynamo levelled when Tomasz Kedziora slammed in the rebound after a Tamas Kadar header was parried by Andre Onana, but Ajax established a two-goal lead before the break.
Hakim Ziyech collected a loose ball on the edge of the box, worked some space on his left foot and found Boyko's top-left corner via a deflection off Kadar's head.
Dusan Tadic then turned in a low cross from Nicolas Tagliafico in the 43rd minute to put the Eredivisie giants in a commanding position in the tie, with Dynamo unable to find a second away goal.
AEK assumed a dominant position after their first leg in Hungary, goals from Viktor Klonaridis and Anastasios Bakasetas capitalising on a 22nd-minute red card shown to Szabolcs Huszti.
Bakasetas was dismissed himself early in the second half and Danko Lazovic gave Videoton hope of a fightback, but AEK has a cushion to take into next week's return in Athens.
In Thursday's (AEST) final tie, Young Boys could not hold on to a second-minute lead earned by Kevin Mbabu's strike, with Mislav Orsic giving Dinamo Zagreb an away goal in a 1-1 draw at the Stade de Suisse.