In a first leg full of missed opportunities at the Olympic National Sports Complex on Thursday, Zozulya made the most of his chance as Dnipro also denied Ajax a valuable away goal.
After Thulani Serero and Yevhen Seleznyov both wasted gilt-edged openings inside the first 10 minutes, Zozulya opened his Europa League account for the season, but will miss the return game after picking up a second-half yellow card.
The forward fired past Jasper Cillessen after half an hour to give Dnipro the lead, although Ajax should have been level at the break – Joel Veltman conspiring to miss in front of an open goal.
Frank de Boer was able to recall Arkadiusz Milik following a hamstring problem, but his side drew blanks going forward as Myron Markevych's men saw out the victory with relative comfort.
Ajax started strongly in Kiev and should have led after five minutes when Thulani Serero sprung the offside trap, only to see his attempted lob thwarted by Denis Boyko.
Dnipro then wasted a golden opportunity to take the lead when Cillessen failed to control Veltman's hefty backpass.
However, Seleznyov prodded the loose ball wide, as two of the half's best chances were both wasted early on.
The hosts gradually got on top and broke the deadlock when Zozulya found space in the area following Yevhen Konoplyanka's cutback and fired past Cillessen.
A divot in the pitch appeared to help the ball beyond the Ajax goalkeeper, with Cillessen then quickly called on to keep Seleznyov's long-range effort out.
Veltman's difficult half continued as he scooped Davy Klaassen's knockdown over the crossbar with an open goal to aim and Dnipro aimed to punish the visitors' profligacy when Seleznyov again fired at Cillessen from distance after the break.
The Netherlands international continued to be busy, this time saving Artem Fedetskiy's testing close-range header before Douglas was required to clear Ricardo van Rhijn's delivery, with Milik lying in wait.
Brazilian defender Douglas was again on hand to clear the danger from Anwar El Ghazi's cross, as Dnipro showed why their clean sheet record at home stretches back three games to the start of December.
In contrast, Ajax's seven-game unbeaten run in all competitions came to an end as they were made to lament their costly first-half misses with Dnipro denting the Dutch champions' hopes of winning silverware this season ahead of the second leg in Amsterdam later this month.
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