Yevhen Konoplyanka's extra-time strike booked Dnipro's place in the quarter-finals of the Europa League on away goals despite a 2-1 second-leg defeat to Ajax in Amsterdam.
Riechedly Bazoer put Ajax ahead in the 60th minute to level the tie at 1-1, however neither side could find a winning goal before the 90 minutes were up.
Dnipro, who had looked dangerous throughout the match, then claimed what proved to be the decisive away goal in the 97th minute when Konoplyanka calmly broke to the left edge of Ajax's box before unleashing a shot past Jasper Cillessen.
Mike van der Hoorn scored for Ajax late in the second period of extra-time to set up a tense finale, but Dnipro held on to go through after a 2-2 aggregate draw.
Ajax knew they needed to chase the tie after starting the second leg a goal down and Anwar El Ghazi almost gave them the perfect start when his 20-yard strike troubled Denys Boyko in the seventh minute, with the visiting keeper forced to parry the effort away.
Bazoer and Arkadiusz Milik cleared two Dnipro corners before Ajax keeper Cillessen caught Nikola Kalinic's curling shot from 20 yards.
Cillessen easily punched clear from a Junior Egidio effort just after the half-hour mark before Douglas Silva's weak shot was easily gathered by the home stopper.
Milik had the best opportunity of the half to break the deadlock shortly before the interval when he got in between the two centre-halves from a first-time cross and headed just wide in the 43rd minute as Ajax searched for the goal that would keep their European hopes alive.
That breakthrough finally came in the 60th minute when Bazoer fired into the bottom-right corner from the middle of the area with a powerful shot to put the Dutch club back on level terms.
With the score tied at 1-1 on aggregate and both side's inability to find another goal, the game went into extra periods.
Dnipro captain Konoplyanka did score, though, in the 97th minute after a break down the left and race to the edge of the area which left the Ajax defenders looking clueless.
It put the visitors on the brink of qualification and meant Ajax needed to score two goals to progress thanks to the away goal rule.
They were given brief hope in the final minutes when Van der Hoorn headed past Boyko in the 117th minute, but they could not find the second goal they needed to progress.