Wayne Rooney headed the only goal of the match on 48 minutes after mistake from Ukraine goalkeeper Andrey Pyatov.
But there was huge controversy when John Terry cleared a Marko Devic shot that had crossed the line. None of the officials, including the additional assistant referee standing just metres from the goal, appeared to see the incident.
After victory, England collected seven points and topped Group D and now faces Spain in quarterfinal match.
In the second match, Sweden claimed a 2-0 victory over France and condemned Laurent Blanc's side to a daunting quarterfinal match with Spain.
Zlatan Ibrahimovic (on 54 minutes)and Sebastian Larsson (90) were on target for Sweden in the match.