The Spanish side looked destined to come away from Cyprus with a draw, but the Chilean and the Algerian scored late to seal the win
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 would worked in their favor. However, it took until the 79th minute to break through the dogged defense of Oleh Blokhin's team, before a second came 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 26 minutes in 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 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 onto.
Immediately after halftime, 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.
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 tantalizing 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 the 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 second leg at Mestalla.