Juan de la Cruz Ramos Cano's outfit never looked in danger of losing to AIK, who had previously picked up just four points and had no hope of progressing.
Nikola Kalinic put the home side ahead from the spot after 19 minutes and Roman Zozulya put the Ukrainians two ahead just before half-time.
The striker grabbed his second after the restart, before Serhiy Kravchenkoas completed the scoring as AIK exited the competition bottom of the group.
Only a defeat and a Napoli victory could prevent Dnipro from topping the group, but that scenario never looked likely after they took the lead after 20 minutes.
They were given a helping hand by their Swedish opposition, as Yevgen Konoplianka's corner was punched in the area by full-back Martin Lorentzson.
Striker Kalinic did the rest from the spot as his effort straight down the middle beat Ivan Turina for his second goal in the competition.
The hosts were two goals up seven minutes before the break when Zozulya got on the end of a Konoplianka cross, placing his effort into the bottom right-hand corner.
The game was over just six minutes into the second half before Zozulya grabbed his second, again beating Turina with a low effort.
And Kravchenko finished the scoring with a controlled volley from inside the area as AIK endured a miserable night in Ukraine.