Nick Viergever and Amin Younes grabbed extra-time goals at Schalke to send Ajax through to the UEFA Europa League last four.
Ajax survived an heroic Schalke fightback and the dismissal of Joel Veltman as it reached the semi-finals of the UEFA Europa League despite going down to a 3-2 second-leg defeat at Veltins-Arena.
Nick Viergever was the hero for the Dutch side, the defender deflecting Matija Nastasic's attempted clearance into the net in the 111th minute, before Amin Younes struck in the closing seconds to finally settle a see-saw tie.
Schalke had rallied from a 2-0 first-leg deficit to force extra-time, Leon Goretzka and Guido Burgstaller scoring in the space of three second-half minutes to drag the Bundesliga team level on aggregate, although the former's night came to an early end because of a head injury.
Veltman also failed to see out the match, the defender dismissed with 10 minutes to go in normal time as Ajax, winner of the UEFA Cup in 1992, seemingly collapsed down the stretch.
Daniel Caligiuri put Schalke on course for the last four when he nodded in a teasing Sead Kolasinac cross to make it 3-2 on aggregate, only Viergever and Younes to strike late and book Ajax's place in Friday's draw.