It was the win the French desperately needed to put themselves in sight of the quarters.
Lightning forced officials to suspend the match for an hour at the Donbass Arena.
But when action resumed neither side could break the deadlock until the second half.
On 53 minutes Franck Ribery escaped down the left flank at speed. He cut the ball square to Karim Benzema who quickly offloaded to Jeremy Menez.
With the Ukraine defence turned inside out the Paris St Germain player pulled the ball to his left foot and unleashed a low drive past Andriy Pyatov.
With the Ukrainians still in shock from the first goal Yohan Cabaye made it two nil two minutes later capping off a dominant period France.
After latching onto Benzema’s through ball the Newcastle United midfielder shrugged off a weak challenge from Oleg Gusiev to coolly blast his shot home.
Although Ukraine remained a threat in the closing stages France proved too strong and held on for the win.