The Three Lions, managed by Roy Hodgson, had followed up a draw with France by dramatically defeating Sweden in Kiev, and the door was open for England to avoid having to face Spain in the quarter-finals.
Hodgson had been without the suspended Wayne Rooney for the opening two games, but despite replacement Andy Carroll producing an all-round impressive showing against Sweden, Rooney was immediately restored to the side alongside Manchester United teammate Danny Welbeck in attack.
The encounter in Donetsk started off as a timid affair, but Ukraine soon began to find their rhythm in England's half and Scott Parker was forced to make an excellent block to deny Marko Devic's shot finding its way on target.
Minutes later, John Terry followed suit to get in the way of a Yevhen Konoplyanka strike before Oleg Gusev capitalised on a mistake from Ashley Young to call Joe Hart into action by having the England stopper sprawling across his goalline to keep the score at 0-0.
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However, that near miss saw England begin to improve, and after a couple of crossing opportunities had been wasted, Rooney spurned a golden chance to put his side ahead when, after getting on the end of a Young delivery, he somehow headed the ball wide from six yards out.
A goal would have eased the nerves in the England camp, but the miss only galvanised Ukraine and two minutes later they attempted to deliver a sucker-punch through Andriy Yarmolenko but his bending effort was well dealt with by Hart.
England were aware that they were 45 minutes away from a place in the last eight, and they took a giant stride to making sure of their quarter-final spot when Rooney atoned for his lack of a clinical touch in the first half by nodding his team in front at the start of the second.
The ball was worked out to Steven Gerrard on the right-hand side, who quickly set about whipping a bending cross towards the back post where Rooney capitalised on a glaring error from Andriy Pyatov to head in his first goal in a major tournament for eight years.
The pass-and-move game that Hodgson had hoped to see was beginning to get the better of their opponents, but against the run of play, Ukraine almost equalised through Artem Milevskiy, but he somehow managed to head the ball over the crossbar from three yards.
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Two minutes later, the co-hosts should have been level when Devic forced the ball over the line despite the best efforts of Hart and Terry, but despite the ball going over the line, the officials adjudged that the Chelsea defender had got back in line to clear it from under the crossbar.
Ukraine continued to attack in numbers, but they were almost caught on the break by England. James Milner sent in a cross that was parried away by Pyatov but the ball fell to Ashley Cole, who brought a decent stop out of the goalkeeper.
The final 15 minutes saw Ukraine, who needed three points to advance, push men forward, with Konoplyanka going closest after sending a swerving effort towards Hart's goal, but they couldn't breach England's backline as Hodgson's men held on to secure their place in the quarter-finals.
France's 2-0 loss to Sweden resulted in England finishing in top spot in Group D, which saw them progress through to a last-eight showdown with Italy, who had beaten Republic of Ireland in their final opening-round match to qualify.
It wasn't to be for England who, after keeping Italy out for 120 minutes, lost 4-2 in a penalty shootout after Young and Cole had failed to net from the spot.