The Spanish side looked set to come away from Cyprus with just a draw, but they struck twice in the dying minutes to nick a valuable victory
Los Che, heading into the game on the back of a five-match unbeaten streak in La Liga, may have hoped that playing their away tie in Cyprus due to political tensions in Ukraine could have worked in their favour but took until the 79th minute to break through the dogged defences of Oleh Blokhin's team, with a second coming in stoppage-time.
In fact, the opening 20 minutes saw Dynamo Kiev look the more likely to take the lead as Nigerian forward Brown Ideye headed marginally wide before the referee called play back for a free kick to the visitors.
At the other end, Jonas had the best chance of the match as of 26 minutes when Jeremy Mathieu looped a cross to his feet, but Ukrainian goalkeeper Aleksandr Shovkovsky came off his line to swipe the ball away from the Brazilian.
Juan Antonio Pizzi's men continued to exploit the wing for their chances as they went into the ascendancy in the final 20 minutes of the first half, with Jonas constantly lingering on the last man in search of a cross that he could latch on to.
Immediately after half-time, however, Jeremain Lens went closer than anyone in 48 minutes had by connecting with Danilo Silva's cross, but his shot cannoned over the crossbar.
The next 15 minutes were characterised by a stop-start nature as defender Domagoj Vida then Shovkovsky needed treatment for injuries, with the latter forced off.
Two chances in quick succession nearly saw los Che take the lead as the game burst into life with 14 minutes on the clock, with substitute goalkeeper Aleksandr Rybka doing excellently to deny Dani Parejo then Seydou Keita from close range.
Three minutes later, Dynamo should have held the lead but Ideye could not make contact on Silva's tantalising cross.
That failed attack cost Blokhin's men dearly as Valencia counterattacked and won a corner, which Parejo whipped on to Vargas' head and the Napoli loanee guided it into the back of the net.
Dynamo's spirit was hit hard by the late goal and Vargas almost doubled his lead shortly afterwards, thumping off the foot of the post after a terrific ball from Joao Pereira.
Pizzi's charges grabbed their second goal in stoppage time as Feghouli nestled Pereira's cross into the back of the net via a deflection to give the Spanish side the edge going into the tie at Mestalla.