Wayne Rooney marked his England return with the goal that secured a place in Euro 2012's last eight - but it was a rough passage eased by helpings of good fortune and controversy against Ukraine.
England manager Roy Hodgson instantly restored Rooney after a two-match suspension in place of Andy Carroll with orders to make a belated mark on the campaign after sitting out the draw against France and victory against Sweden.
And after missing a simple header in the first half, the Manchester United striker ensured England topped Group D to set up a quarter-final meeting with Italy in Kiev on Sunday.
England could have met world and European champions Spain but that eventuality was avoided by
Sweden's 2-0 win against France,
and Rooney's first goal in a major tournament since scoring twice in the 4-2 victory over Croatia in Lisbon at Euro 2004.
"We hope Wayne Rooney will get fitter. Steven Gerrard is a massive plus and if he can keep this form then England have a chance. We're not playing great football, we're just getting results."
Ukraine, however, will complain long and hard about a contentious second-half incident when Marko Devic's shot clearly crossed the line before it was scrambled away by John Terry, only for the officials to remain unmoved.
The incident immediately revived the debate about goal-line technology, with a final decision on whether it is introduced expected to be taken in Zurich on 5 July.
England will regard it as a measure of justice for
Frank Lampard's disallowed goal against Germany in Bloemfontein at the 2010 World Cup
- but it was also an illustration of how they rode their luck for long periods in front of a predictably partisan home crowd.
But once again Hodgson's men found a way to get the result they required and there is a real air of respectability about their campaign even though they had to survive a first-half siege from a Ukraine side desperate for the win they needed to progress.
Oleg Blokhin's side lost the talismanic Andriy Shevchenko to the substitutes' bench because of a knee injury but still showed enough to put England through real turmoil in spells.
A lack of match sharpness was perhaps to blame for Rooney squandering England's best chance after 27 minutes.
It appeared he only had to make clean contact with Manchester United team-mate Ashley Young's cross to score but his far-post header lacked conviction and went tamely wide of keeper Andriy Pyatov's goal.
Either side of Rooney's fluffed chance, it was a tale of Ukrainian domination as they attacked England down both flanks and showed the greater fluidity of the teams.
Scott Parker was desperately urging England's players to keep possession - but it was easier said than done amid waves of Ukraine attacks and it needed a penalty area block from the Tottenham midfield man to thwart Devic.
England keeper Joe Hart had to save smartly from the dangerous Andriy Yarmolenko, who also raised the hopes of the Donetsk crowd as he evaded several challenges in the area before running out of space.
However, Rooney made no mistake with his second headed opportunity, Steven Gerrard's delivery from the right once again the creative source. The cross took two deflections and slipped from the grasp of Pyatov for a simple far-post header from the Manchester United striker.
The crowd was momentarily silenced but Ukraine refused to lose heart - and they were robbed of an equaliser when once again an effort that had crossed the line was not spotted by officials.
Artem Milevskiy should have done better than send a header wide but the real controversy came when Hart partially stopped Devic's effort and Terry desperately scrambled back to hook the ball off the line.
The Ukrainians immediately demanded a goal and their claims were vindicated as replays showed the ball crossed the line before Terry's intervention.
There was still time amid the drama for Ashley Cole to almost mark his 97th cap with a goal but the erratic Pyatov made a fine recovery save after another inelegant attempt to deal with a cross.
With 20 minutes left it was time for the entrance of Ukraine's great sporting icon Shevchenko.
He received a thunderous ovation as his country looked to him to rescue their Euro 2012 campaign but it was a task beyond even the veteran striker, who was soon booked for a rash challenge.
Before the game manager Hodgson had said England could dream a little - ahead of the confrontation with Italy in Kiev, they can now afford to dream a little more.
- 01 Hart
- 02 Johnson
- 03 Cole Booked
- 06 Terry
- 15 Lescott
- 04 Gerrard Booked
- 11 Young
- 16 Milner (Walcott - 70' )
- 17 Parker
- 10 Rooney (Oxlade-Chamberlain - 87' )
- 22 Welbeck (Carroll - 82' )
- 13 Green
- 23 Butland
- 05 Kelly
- 12 Baines
- 14 Jones
- 18 Jagielka
- 07 Walcott
- 08 Henderson
- 19 Downing
- 20 Oxlade-Chamberlain
- 09 Carroll
- 21 Defoe
- 12 Pyatov
- 02 Selin
- 03 Khacheridi
- 20 Rakitskiy Booked
- 04 Tymoschuk Booked
- 06 Garmash (Nazarenko - 78' )
- 09 Gusev
- 11 Yarmolenko
- 19 Konoplienka
- 15 Milevskiy (Butko - 77' )
- 22 Devic (Shevchenko - 70' Booked )
- 01 Koval
- 23 Goryainov
- 05 Kucher
- 13 Shevchuk
- 17 Mykhalyk
- 21 Butko
- 08 Aliev
- 14 Rotan
- 18 Nazarenko
- 07 Shevchenko
- 10 Voronin
- 16 Seleznyov
Ref: V Kassai