Dynamo Kiev winger Yarmolenko, who has been linked with several English clubs, made the breakthrough in the 28th minute after latching on to Ruslan Rotan's chipped free-kick.
Mykhaylo Fomenko's side also beat Cyprus 1-0 with a set-piece goal four days ago when Wales, who were again without the rested Gareth Bale, were held 1-1 at home by Northern Ireland.
Ukraine, who qualified for the Euros through the playoffs, face world champions Germany, Poland and Northern Ireland in France, while Wales tackle England, Russia and Slovakia.
Wales coach Chris Coleman made six changes and used a 5-3-2 formation which looked solid until Ukraine struck with a goal Wayne Hennessy conceded at his near post after the unmarked Yarmolenko's close-range strike with their only shot on target.
Welshman Tom Lawrence forced home keeper Andriy Pyatov to tip the ball over the bar with a powerful angled shot in the first half and Joe Allen also threatened for Wales.
Denys Garmash almost made it 2-0 with a header wide of the far post from a set piece while efforts by Wales substitutes Jazz Richards and Joe Ledley were saved in added time.
"Even if we were at full strength, it would still be a tough game for us anyway. We have conceded from set pieces in two games and that is what disappoints me most," said Coleman, who was also without another influential midfielder Aaron Ramsey.
"It was a pretty good test for us before Russia and Slovakia (at the Euros)," he added.
(Editing by Ken Ferris)
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