Last-placed PSV took the lead through Georgino Wijnaldum's early goal, but Group F leaders Dnipro quickly levelled through Yevhen Seleznyov before Yevgen Konoplianka struck a 74th-minute winner for the visitors.
Dnipro had to play out the closing stages with 10 men following the 84th-minute dismissal of Jaba Kankava, but they held on to secure a qualifying spot along with second-placed Napoli, who beat AIK tonight.
The Ukrainian side threatened first, with Seleznyov's third-minute shot being punched clear by goalkeeper Boy Waterman, but PSV responded with efforts from Timothy Derijck and Wilfred Bouma and it was the Dutch side who took the lead in the 18th minute.
Wijnaldum latched on to a fine through-ball from Atiba Hutchinson before drilling a first-time shot past Jan Lastuvka from the edge of the box.
PSV enjoyed their lead for only six minutes, though, before Dnipro levelled things up.
Waterman had little trouble dealing with a Victor Giuliano effort in the 20th minute, but he was left with no chance soon after as Seleznyov turned in Ivan Strinic's low cross from the right from close range.
Both sides continued to push for a second goal after that, but neither goalkeeper was overly stretched before Lastuvka was called on at the start of the second half to parry a Tim Matavz effort.
That was a good chance for PSV and a goal then could have made all the difference to the 1988 European champions' hopes of staying in the competition.
As it was, they slipped 2-1 down in the 74th minute and there was no way back for Dick Advocaat's men after that.
Dnipro came close to going ahead for the first time in the 70th minute when Seleznyov's shot was tipped round the post by Waterman, and soon after they did net what would prove to be the winning goal.
Konoplianka was the scorer, picking up a pass from Seleznyov before thumping a 20-yard shot into the top corner.
PSV were given late hope when Dnipro midfielder Kankava was booked twice in three minutes, both times for handball, to leave his side to play out the final six minutes with a man less.
The hosts laid siege to the Dnipro goal late on but none of Hutchinson, Antonio Marcelo and Memphis Depay could make the most of their chances as PSV's European adventure came to an end.