The home side, without a few key injured players, took the chance to tinker with their line-up with an eye on the forthcoming European Championships and were rewarded for their first-half domination with Stepanenko's 40th minute winner.
The Shakhtar Donetsk midfielder followed up to finish from close range at the far post after Cyprus keeper Constantinos Panayi had saved Roman Zozulya's header.
Cyprus, whose striker Nestoras Mitidis spurned a great chance in the 20th minute with a weak finish, created a few excellent openings in the closing stages with Nikos Englezou sending a shot just wide and Pieros Soteriou hitting the post.
(Editing by Ian Chadband)
