In the end, England qualified with something to spare and the prize for overhauling France at the top of Group D is a significant one. Italy will represent challenging opponents in the quarter-final on Sunday but the benefits of circumnavigating a date with Spain are plain and Roy Hodgson's players are entitled to think their aspirations of reaching the last four have just been dramatically enhanced.

A semi‑final against Germany or Greece will follow for the winners and England head to Kiev with the kind of confident assurance that would barely have seemed plausible when Hodgson was parachuted into this job, with only a matter of weeks and a handful of training sessions to put together a team of authentic coherence and ambition.

Hodgson has overseen four wins in his five games and the latest, courtesy of Wayne Rooney's decisive contribution, demonstrated the blend of resilience and opportunism that was always going to be necessary to progress. In the process it ensured Ukraine follow Poland, their co‑hosts, in being eliminated from the competition at the first stage, just as Switzerland and Austria were four years ago.

Rooney will cherish this moment, his first goal in an international tournament since Euro 2004, and England will certainly have a better chance to get past Italy now their most prized striker is in confident, scoring form. The big man is back, to borrow Rooney's own phrase, supported by a performance of great substance from Steven Gerrard, some resolute defending from a back four superbly marshalled by Terry and Joleon Lescott – and, yes, the sense that England may suddenly have good fortune on their side.

The mistake from Ukraine's goalkeeper, Andriy Pyatov, for the goal was one thing but the win was tinged with controversy, too. England's opponents can harbour serious grievances about the moment, after 62 minutes, when Marko Devic's shot flicked off Joe Hart and was clearly over the goalline by the time Terry had hooked the ball away. Ukraine needed to win to qualify and an equaliser would have left Hodgson's team facing a late onslaught. These decisions are precisely the reason why Uefa has brought in goalline officials and, for Ukraine, the repercussions were considerable, even if their argument was undermined by an offside decision being missed in the buildup.

Their manager, Oleh Blokhin, was never going to go quietly, inviting one journalist to step outside and discuss his views "man to man" after taking exception to a question about his selection. Even as he walked out, he was still gesturing he wanted to prolong the argument the old-fashioned way. Hodgson's press conference was a far less spiky occasion, in keeping with the new sense of calm that exists after all the controversies, arguments and traumas that have gone before. Hodgson talked of a collective effort but, inevitably, picked out Rooney and Gerrard for special acclaim.

Gerrard, he said, had delivered three man-of-the-match performances in succession, epitomising the spirit that eventually succeeded in turning down the volume inside a loud, partisan stadium.

The Donbass Arena was not the bear-pit, perhaps, that had been anticipated but it was still a challenging environment and, for England, part of the battle was to quell that noise. It needed composure and assurance. More than anything, it required a force of personality.

Hodgson's players were subjected to some prolonged spells of pressure, particularly in the first half, but there was never the slightest sense the crowd could unnerve them.

The win might have been considerably easier if Rooney had not tempted us to believe, in the opening half, this was going to be one of those nights that could be added to his portfolio of England disappointments. His first chance came after 28 minutes and it was a horrible miss, from the best cross Ashley Young has delivered in this tournament.

Rooney's header flashed wide and it was alarming to see the lack of confidence with which he attacked the ball. Unmarked, six yards out, it was the sort of chance he would have taken as a matter of routine for Manchester United last season.

Ukraine were the more dangerous team at that point, breaking from midfield and moving the ball quickly, but the goal gave England a new impetus in the second half. The replays will not make good viewing for Pyatov, who was deceived by two slight deflections and let Gerrard's cross squirm through his arms. Once again, though, it was another high-quality delivery from Gerrard, who is making a habit of setting up goals with his range of crossing. On this occasion he preceded it by deceiving his nearest opponent, Yevhen Konoplyanka, to create the space. It was brilliant play and Rooney showed good anticipation to capitalise on the goalkeeper's mistake and head into an exposed net.

Ukraine had to attack with even greater endeavour now, leaving more spaces to exploit. Soon afterwards Gerrard intercepted a corner and sent Rooney running clear from inside his own half, only for the striker to check back when through on goal. Later, Pyatov had to keep out Ashley Cole's snap-shot.

The crowd were soon imploring for Andriy Shevchenko's introduction, the Ukraine talisman restricted to a substitute's role because of a knee problem. Artem Milevskiy squandered an unmarked header and Ukraine could also reflect on Hart's save from Milevskiy's shot. Mostly, they would think back to the goal that never was. England made the most of their luck and Sweden's defeat of France made it all the more gratifying.