The German side took the lead after 12 minutes when Juan Arango picked out Alexander Ring inside the box and the midfielder curled his shot past Maksym Koval.
Kiev responded well to the goal and were rewarded on 28 minutes when Taras Mikhalik collected a loose ball following a corner before unleashing a powerful effort into the top corner of the Monchengladbach goal.
The Ukranian found a second away goal before half-time to give themselves a big boost heading into the break as Andriy Yarmolenko was put through on goal and the striker made no mistake by sliding the ball past Marc-Andre Ter Stegen.
Monchengladbach improved in the second period but failed to force an equaliser with Granit Xhaka being denied a goal on two occasions by Koval.
As the game entered the final stages, Kiev found a goal that could prove to be crucial in the tie as Luuk de Jong put the ball past his own goalkeeper to improve the Ukranian side's victory.