A goalless draw at Pittodrie in the first leg a fortnight ago had left the tie evenly poised.
Dnipro made a fast start and after three minutes Dons keeper Jamie Langfield made a smart save after Dmitry Lyopa had latched on to Serhiy Nazarenko's cross-cum-shot.
Eight minutes in Jamie Smith found space in the inside left channel, but his left-foot shot from the edge of the area was deflected away from danger.
Andriy Vorobey almost connected with Lyopa as the home side hit back, but, with 27 minutes on the clock, Aberdeen took the lead on the night and on aggregate.
Rickie Foster made time and space on the left and his cross to the middle of the area was met by a flying Darren Mackie, whose header from close range gave Vyacheslav Kernozenko no chance.
Dnipro dominated the rest of the first half as they went chasing an equaliser, but the Aberdeen defence stood firm to defend their narrow advantage.
The Ukrainian hosts continued to hold the upper hand at the start of the second half, without seriously testing Langfield.
Just past the hour a Konstyantyn Kravchenko corner from the right was headed against the top of the crossbar by Andriy Rusol and soon after Langfield tipped over a superb drive from distance by Kravchenko.
Bohdan Shershun fired over from close range following another corner, before Dnipro finally broke through as another flag-kick caused chaos and an attempted clearance was blocked by Vorobey and his touch rifled the ball past Langfield.
Nazarenko lashed a 30-yard drive against the crossbar as Dnipro went in search of a winner and then Langfield turned a Kravchenko blockbuster against the bar to keep the Dons in front by virtue of their away goal.
He also tipped away a long-range effort deep into stoppage time to ensure a night of celebrations for Jimmy Calderwood and his Dons staff.