Ajax defeated Panathinaikos 13-12 in a Europa League penalty shootout on Thursday with 34 kicks from the spot required to settle the tie.
Both teams took a total of 17 penalties each before Anton Gaaei slotted his attempt home to secure a memorable victory.
Ajax goalkeeper Remko Pasveer saved five penalties and even scored one himself.
“It was incredible,” said Ajax coach Francesco Farioli. “The spirit and commitment of the team were great tonight. We are not perfect, but we cannot say that the players did not give everything.”
He added: “But the match was fantastic. It is difficult to go into a penalty shootout after such a match. It may have taken a little longer, but we have taken an important step again.”
Ajax had led 1-0 from the first leg but the Greeks stayed alive thanks to an 89th-minute goal from Tete which sent the tie into extra-time.
The Dutch side go on to face Jagiellonia Białystok of Poland in the play-off round next week.