Winger Andriy Yarmolenko opened the scoring with a low shot into the far corner of the net in the 22nd minute that sparked wild celebrations at a packed Lviv Arena.
Yarmolenko also played a part in the second goal in the 54th minute, striker Yevhen Seleznyov converting his cross to supply the finishing touch to a swift counter-attack.
Seleznyov could have added a third goal 15 minutes later when he scuffed his shot when well-placed but Ukraine will still be in a strong position in Tuesday's second leg to book their ticket to the finals in France.
Slovenia provided little threat up front although Branko Ilic fired just over the bar from the edge of the penalty area in the first half following a clever header from Milivoje Novakovic.
The visitors, bidding to repeat their Euro 2000 playoff victory over Ukraine, never looked like getting back into the game after the break.
Keeper Samir Handanovic, captaining Slovenia, produced a stunning save from a header by Denys Gamrash before Seleznyov struck the woodwork in the 69th minute.
Ukraine coach Mykhaylo Fomenko warned his players not to get carried away by the margin of victory.
OFFSIDE CLAIM
"We have only played the first leg." he told national television. "We could have scored a third goal and I'm glad Slovenia did not capitalise on our mistakes.
"I think my players understand what they have to do and I should not need to find any additional words (of motivation) for the second leg."
Ukraine President Petro Poroshenko and Slovenia counterpart Borut Pahor watched the game from the stands.
"The President greeted us in the dressing room after and wished us good luck for the return game," said defender Evhen Khacheridi.
Slovenia coach Srecko Katanec, who was also at the helm for the Euro 2000 playoff, blamed the referee for the second goal.
"We started off with purpose but couldn't keep it going," he said. "I think the second goal was offside so the luck was not on our side today.
"The result is hard for us but there is nothing impossible in football. We will do our best to snatch a win with the right scoreline."
A minute's silence was observed before kickoff in memory of the 129 people killed and 352 wounded during the attacks in Paris on Friday evening.
(Editing by Tony Jimenez)
Share
