Everton came from behind to see off their Ukrainian opponents thanks to a Steven Naismith strike and Romelu Lukaku's late spot kick to take a slender lead into the second leg.
Things got off in the worst possible way for Everton as just a quarter of an hour in Dynamo Kiev grabbed a crucial away goal thanks to a superb Oleh Gusev strike which flew past Tim Howard following a Andrey Yarmolenko corner.
Everton responded well after a poor start though and were back on terms six minutes before half time when after good hold up play from Lukaku, Steven Naismith whipped the ball into the far corner right footed from the left side of the box.
Everton pushed for a lead to take into the second leg in the second half of this game and found it when Danilo Silva handled Seamus Coleman's cross from the right allowing Lukaku the chance to win the game, which he did rolling the ball down the middle of the goal to become Everton's top scorer in Europe.
Kiev slightly had the better of things in the first half and could have had more than one away goal thanks to the long range ability of Serhiy Sidorchuk who fired just over and forced Howard into a decent save with thirty yard efforts on goal.
Kevin Mirallas had Everton's only real main chance of the first half just before half time when he rounded the keeper down the right only to go to far wide and not be able to find the waiting Lukaku in the middle.
Shovkovskiy in the Dynamo goal was a lot busier man in the second half with Antolin Alcaraz from distance and Naismith with his head forcing the keeper to work, substitute Arouna Kone probably had the best chance though but he was smothered by the on rushing keeper after a good ball by James McCarthy.
Kiev were still a threat down the other end Dieudonne Mbokani should have done better than just heading into the side netting from close range but Everton went onto win it and take a slender advantage to the Ukraine for the second leg this time next week.