Dynamo Kiev striker Andriy Yarmolenko bagged a hat-trick as Ukraine left Luxembourg's Stade Josy Barthel with all three points on Saturday.
Yarmolenko broke the deadlock in the 33rd minute before the 25-year-old completed his treble haul with another two goals in quick succession in the second half.
Ukraine have now won three games in a row to sit third in Group C, level on nine points with defending champions Spain, and three adrift of pacesetters Slovakia.
Coach Fomenko was pleased with the character demonstrated by his side, who were hampered by injuries in the lead up to Saturday's fixture.
"At the beginning of the match Luxembourg were on top a bit and had three good chances to score," Fomenko said afterwards.
"We reacted with discipline and thanks to that we got the first goal. In the end the result says that we were disciplined.
"Our way of playing tonight shows that we were much better than against Slovakia [a 1-0 home defeat in September].
"It was not easy to prepare for this game because we had many injured players and this has been the case since the beginning of our Euro campaign."
