France's Laurent Koscielny and the home side's Oleksandr Kucher were sent off in injury time asUkraine took a step towards securing their second World Cup appearance after reaching the quarter-finals in 2006.
The visitors tried to keep possession but Ukraine were the most dangerous side and Francegoalkeeper Hugo Lloris, who started the game 12 days after suffering a concussion, made his first block from Yarmolenko's crossed shot in the seventh minute.
FIFA Ballon d'Or hopeful Franck Ribery was closely marked as Les Bleus failed to create clearcut chances and at the back their weak spot was the left side with centre half Eric Abidal and full backPatrice Evra struggling to cope with Yarmolenko's pace.
In the 61st minute, Zozulia squeezed his shot just under Lloris from Edmar's touch to put the home side ahead.
Giroud, who failed to muster a chance, was substituted by Benzema 20 minutes from time.
It was Ukraine, however, who scored again when Yarmolenko converted a penalty after Koscielny had fouled Zozulia in the box.