The Argentinian Maxi Rodriguez put Atletico ahead and, though Dimitris Salpingidis levelled, second-half goals from the Uruguayan Diego Forlan and Sergio Aguero, another Argentinian, made it 3-1.
Yet another Argentinian, Sebastian Leto, gave Panathinaikos some hope as he struck for the home side with 16 minutes remaining.
Debrecen of Hungary are just one step from a first appearance in the group stage, Peter Czvitkovics's 76th-minute winner giving them a 2-1 win over Bulgarian champions Levski Sofia. Laszlo Bodnar had given them the lead, only for Cedric Bardon to level.
Maccabi Haifa beat Salzburg 2-1 in the night's other game.
Alexander Zickler cancelled out Mohammed Ghadir's opener, but Shlomi Arbeitman restored the Israel champions' advantage with six minutes remaining.
The second legs of Wednesday's games will be played Tuesday.