After a minute's silence had been observed ahead of a game switched to the neutral venue of Cyprus due to the ongoing unrest in Ukraine, Yarmolenko broke the deadlock on 12 minutes with a fine finish after brilliant work from his Dynamo Kiev club-mate Denys Garmash.
The US rallied after half-time, with Alejandro Bedoya and Jozy Altidore both wasting good opportunities, before Ukraine substitute Devic raced away to wrap up the win 22 minutes from time.
The build-up to the international friendly at the Stadio Antonis Papadopoulos was further overshadowed after all of last weekend's top-flight fixtures in Cyprus were postponed following a bomb attack on referee Leontios Trattou's car.
However, Trattou took charge of this clash, which saw US coach Jurgen Klinsmann name a predominantly European-based team, with Clint Dempsey the only MLS representative in the German's team.
Klinsmann has just one more match before deciding on his FIFA World Cup squad, and Ukraine - who missed out on Brazil 2014 by losing in a qualification play-off against France - have given him plenty to think about ahead of their opening tournament fixture against Ghana on June 16.
Mikhail Fomenko's side got off to the ideal start as when Garmash forced a save out of Tim Howard, before pouncing on the rebound and squaring for Yarmolenko to finish.
Defender Oguchi Onyewu then almost marked his return to the American team with an own goal, as he nearly turned a fizzing Yarmolenko cross into his own net.
Klinsmann's side struggled to show any attacking intent for much of the first period, but looked more lively after the interval.
First Bedoya saw an effort defelected wide, before Altidore powered Cameron's cross over the bar.
In contrast to their first-half display, Ukraine looked sloppy and Bedoya nearly punished goalkeeper Andriy Pyatov's mistake, but failed to hit the target.
Devic made an almost immediate difference when he came on after 65 minutes, though, smashing home the rebound after Howard had saved his initial effort just three minutes after entering the fray.
Substitute Aron Johannsson nearly pulled one back for the US late on, but saw his crashing volley cleared off the line as Klinsmann's final World Cup preparations got off to an inauspicious start.
