The victory was in contrast to coach Laurent Blanc's continued assertions that France should not be regarded among the tournament favourites although on this display they are.
While the omens seemed to be against them - before the match started a burst of lightning and an immediate thunder crack when La Marseillaise was playing momentarily halted the playing of the French national anthem - France ended the night stretching their long unbeaten record to 23 matches.
Just five minutes after kick-off it looked like they, and everyone else, might have to wait until Saturday for the outcome as conditions worsened so quickly that Dutch referee Bjorn Kuipers halted the game for the players' safety.
But the storm gradually passed, the pitch was cleared of water and the teams came out to serve up yet another thrilling match in a tournament that has gone from strength to strength since it began a week ago.
Ukraine, inspired by their opening 2-1 win over Sweden, were unrecognisable from the team that lost 4-1 to France in a friendly in the same Donbass Arena almost exactly a year ago.
With the predominantly yellow-shirted crowd cheering their every move, the hosts tore into France but, apart from two rasping shots from Andriy Shevchenko who scored both goals in the win against Sweden, France held firm.
Blanc's team came into the game with two contrasting statistical quirks to their name.
Unbeaten for 22 matches, they had, however, failed to win any of their previous eight matches in tournament finals covering Euro 2008 and the 2010 World Cup.
But once they soaked up the best Ukraine had to offer, man of the match Franck Ribery and the hugely effective Karim Benzema took a grip of the game and steered France to an ultimately straightforward win after their opening 1-1 draw with England.
Ribery, having one of his best matches for France since the 2006 World Cup when they last won a tournament game, weaved and created chances for his front men, Samir Nasri always looked dangerous and Jeremy Menez, picked ahead of the dropped Florent Malouda, added pace and dynamism.
Menez did superbly well to make the breakthrough after 53 minutes when he cleverly moved into space after a ball from Benzema and sent a left-foot shot past wrongfooted Ukraine goalkeeper Andriy Pyatov.
Three minutes later the game was as good as over when Yohan Cabaye scored his first goal for France, twisting his way past Oleh Gusyev before firing home.
Ukraine have now failed to win all four games they have played at the stadium, and the early cheers from their fans turned to jeers at the end as their hopes trickled away on the greasy pitch.
Coach Oleg Blokhin was not happy with the way the crowd turned on his men.
"It's not fair to only support your team when you are winning," he grumbled. "We have the impression if we are winning everything is fine, if not we should all be shot."
France coach Blanc told a news conference: "We scored two goals, we could have had more.
"Six years without a win (in a major competition) is a very very long time. I hope the next one won't be in six years, otherwise I will not be there to talk about it, I would be fired before."
France's next game is against Sweden next Tuesday. Another win then and even Blanc might have to admit their chances are better than he is letting on.
