England qualified from Group D as winners on Tuesday night, recording a 1-0 win over co-hosts Ukraine to set up a quarter-final clash with Italy.
The narrow win and France's 2-0 defeat to Sweden means Roy Hodgson's side avoid defending champions Spain for a place in the semi-finals.
England made a bright start to the game but Andriy Yarmolenko nearly found himself through on goal for Ukraine inside eight minutes, only for John Terry to quickly prevent him from getting a shot on target.
Hodgson's men had looked comfortable in the first few minutes, but as the game reached the 15 minute mark, they had created very little and at times were starting to look a little unsettled.
Ukraine coach Oleg Blokhin was already urging his players to move forward, although they needed little encouragement as the co-hosts looked the more likely side to open the scoring.
As the game passed the half hour mark, England had done a decent job at containing Ukraine, although going forward, they had still created few opportunities in open play.
But the Three Lions should have taken the lead through Wayne Rooney, who got on the end of an Ashley Young cross only to head wide from six yards out when he should have found the back of the net.
Ukraine went on the attack immediately and created another good chance when Yarmolenko forced a good save out of Joe Hart, as the co-hosts continued to play the better football through to half-time.
And as the whistle sounded for half-time, England left the pitch with the unwanted statistic that they had failed to register a shot on target in the first half of a game at the European Championships since 1980.
But England made a much better start to the second half and they took the lead - and silenced the Donbass Arena in the process - through Rooney, who got on the end of a Steven Gerrard cross to head home from a yard out after goalkeeper Andriy Pyatov had failed to deal with the delivery.
Ukraine should have gone level just a few minutes later when Artem Milevskiy headed over from close range, then on the hour mark, the co-hosts thought they had finally scored when Marko Devic's shot was partially saved by Hart, then cleared off the line by Terry, with replays suggesting the ball had actually crossed the line. Somehow, the extra official failed to spot this, despite him standing just five yards away, with the debate about goal-line technology likely to continue in the coming days and weeks.
Ukraine, now aware that France had fallen behind against Sweden, continued to swarm forward and brought on Andriy Shevchenko for Devic as the game entered the final twenty minutes.
Yevhen Konoplyanka went close, with his shot from distance swerving and causing Hart problems in the England goal. The Man City keeper could only parry, but club team-mate Joleon Lescott reacted quickly to clear the danger.
Ukraine continued to push forward in the closing minutes of the game, but Hodgson's men held on to record a 1-0 win that sees them finish top of Group D, setting up a showdown with Italy for a place in the last four.