The win ensured England finished the group as winners and will face Italy in their quarter final on Sunday. Roy Hodgson's men win meant they finished ahead of France after they were beaten by Sweden in their final group game.
It was Ukraine that started the better of the sides pinning England in their own half for much of the first period. The first opportunity of the games fell the host's way with Denys Garmash firing a long range effort over the crossbar. The chances didn't stop their for Ukraine as Devic's strike was excellently blocked by Scott Parker.
Devic was involved in much of Ukraine's attacks and was involved in setting up the impressive Andriy Yarmolenko whose shot was comfortably dealt with by Joe Hart.
The inclusion of Wayne Rooney was the only change made by Roy Hodgson, and the Manchester United striker struggled to get into the early stages of the game with poor touches and loose passes.
England's best chance of the half fell to the striker, glancing a header wide from an Ashley Young cross when really Rooney should have done much better.
Ukraine continued their dominance of the half when Oleh Gusev took advantage of Ashley Young's misjudgement of a cross field pass, before shooting narrowly over Joe Hart's bar.
Despite being under pressure for the majority of the first half, it was England and Rooney that took advantage of some sloppy Ukrainian defending to take the lead. After seeing his corner cleared, captain Steven Gerrard received the ball wide from Glen Johnson. The Liverpool captain skipped past one challenge and after seeing the cross deflected twice, Wayne Rooney lurked at the back post to score quite possibly his easiest goal for England.
The goal struck life into both sets of players with Ukraine needing a win to have any chance of qualification. Breaking from a corner Gerrard played Rooney in on goal who could only hold the ball up and set up Milner whose poor shot was easily blocked by the Ukrainian defence.
The chances were coming thick and fast in the game with Artem Milevskiy heading over from a quickly taken corner when really he should have done a lot better. Joe Hart palmed a dangerous looking Gusev cross over the bar before the games controversial talking point took place.
With the whole of Ukraine aggrieved with the decsion, Scott Parker broke forward only to be brought down on the edge of the box. The resulting free kick though was narrowly stuck wide by Rooney.
Joe Hart was once again showed why he is so vital to England, as he magnificently palmed away a swerving 30 yard effort from Konoplienka with Joleon Lescott on hand to clear away the loose ball.
Changes were made by both teams with Hodgson introducing Walcott, Oxlade- Chamberlain and Andy Carroll with Ukraine's talisman Andriy Shevchenko brought on for his final international appearance. Despite the ex-Chelsea's heroics in the country's opening group game against Sweden, he couldn't inspire a comeback this time.
Chances were exchanged late on with Ashley Cole nearly doubling England's lead late on after his shot was excellently palmed away by the Ukrainian goalkeeper. Yarmolenko shot wide for Ukraine when well placed outside the box.
England's solid defensive unit saw the game through and will now face Italy in their quarter final on Sunday in Kiev. With France losing to Sweden in the other group game, England avoid Spain and from no expectation at the beginning of the tournament, England fans are starting to believe.
England: Hart, G.Johnson, Terry, Lescott, A.Cole, Gerrard, Parker, Milner (Walcott 69') Young, Rooney (Oxlade Chamberlain 87'), Welbeck (Carroll 82')
Ukraine: Pyatov, Selin, Khacheridi, Rakitskiy, Tymoshchuk, Garmash (Nazarenko 78') Gusev, Yarmolenko, Konoplienka, Milevskiy (Butko 77'), Devic (Shevchenko 70')
Referee: Viktor Kassai (Hungary)