Devic, Yehven Konoplyanka and Oleg Gusev all sent shots over the crossbar in a frenzied opening, in which England struggled to get out of its own half.
England survived some nervous moments on either side of Devic's disallowed shot, but held on to reach the knockout round with something to spare as Seb Larsson's late goal condemned France to its first defeat in 23 games.
The defeat was made more aggravating by a crucial blown call from the officials, who failed to see that Marko Devic's 64th-minute shot crossed the goal line before it was hooked clear by John Terry, denying Ukraine an equalizer that would have made for a nervy finish to the game for England.