Hibs dominated for long stages of the game but were punished for slack defending at crucial times and the final scoreline flattered the Ukrainians.
After a goalless first leg, Tony Mowbray showed enterprise by including Garry O'Connor, Derek Riordan and Ivan Sproule in his starting line-up.
But the Edinburgh side made the worst possible start when they lost a goal after only 28 seconds.
A poor defensive header from David Murphy fell to Serhiy Nazarenko at the edge of the area and his left-foot volley took a deflection off Guillaume Beuzelin to beat Zbigniew Malkowski.
Hibs hit back and Riordan beat the offside trap and was clean through on Artem Kusliy, but the goalkeeper managed to spread himself to send the ball past for a corner.
The move encouraged Hibs and they equalised after 24 minutes when Riordan was allowed too much space to bring down Gary Caldwell's through pass and hooked the ball past Kusliy.
But Dnipro were back in front within two minutes when Hibs failed to deal with a corner and Bohdan Shershun slammed the ball home after Malkowski had saved his initial header.
Worse was to follow when Dnipro were awarded a soft penalty after Chris Hogg made a naive challenge on Sergei Kornilenko.
Oleh Shelayev made no mistake as he sent Malkowski the wrong way with the spot-kick to put the hosts 3-1 ahead.
It was a wounding blow for Hibs who had taken the game to Dnipro for much of the half but been punished for untidy defending.
The Scottish side dominated the second half but found it hard to break down a Dnipro side content to defend in depth and hit on the break.
Hibs had the ball in the net through Caldwell after 58 minutes but the linesman ruled it offside.
A mistake by Hogg at the other end gave Kornilenko a glimpse of goal but he sliced his shot well wide.
Riordan missed a great chance ten minutes from time when he side-footed wide from six yards after a low cross from Steven Fletcher.
Substitute Olexandr Melashchenko settled it beyond any doubt when he cracked in a fourth from a pass from man-of-the-match Nazarenko and then added a fifth in injury-time with a left-foot volley.