The Ukraine international teed up Nikola Kalinic for the opener after 12 minutes and netted the second himself early in the second half.
Eric Pereira pulled one back with a penalty, but Zozulya had the final word as he laid on two more goals, for Yevgen Shakhov and Serhiy Kravchenko, late on.
Dnipro were already through and Pandurii already out, but the hosts still had top spot in Group E to play for and finished the night just a point behind leaders Fiorentina.
Dnipro meet the Italians in the final group game.
Pandurii came into the game with only pride to play for, but they created the first real chance as Admir Adrovic saw his effort blocked by home goalkeeper Denys Boyko.
The Ukrainians soon established control, though, and Vitaliy Mandzyuk headed wide from Zozulya's left-wing free-kick before Kalinic opened the scoring.
The Croatia striker fired Zozulya's ball in from the left low into the net.
Dnipro continued to press and Kalinic came close to a second when his header was saved by Joao Mingote.
The visiting keeper then did well to parry a Zozulya header, also pushing away a shot from the same player minutes later.
The Romanian side sought to relieve the pressure and Alin Buleica worked Boyko with a shot from the right channel.
Mingote was by far the busier keeper, though, and he had to be alert again just before half-time to turn away a shot from Alexander Kobakhidze.
But Dnipro finally doubled their lead 11 minutes after the break, the influential Zozulya finding the bottom right corner with a shot from 12 yards.
The away side pulled a goal back in the 69th minute, Pereira slotting his spot-kick low into the corner after Oleksandr Svatok had fouled Adrovic.
And Adrovic almost headed them level seven minutes later, but his attempt from a Pereira cross was blocked by Boyko.
Any hopes of a fightback were ended by Dnipro's third in the 86th minute as Shakhov finished low from Zozulya's pass.
And Zozulya was the mastermind behind his side's fourth in the 89th minute, Kravchenko slamming home his pass to put the seal on the victory.