Roy's boys through with Rooney strike.
Roy Hodgson would have been delighted as his star striker came back from a two game suspension with a precious header.
Having already failed to take a glaring first-half chance, Rooney could not miss as Ukraine keeper Andriy Pyatov failed to gather a dangerous low cross from Steven Gerrard which took two deflections.
From barely a yard, Rooney thus scored his 29th England goal to nudge one behind Nat Lofthouse, Tom Finney and Alan Shearer, who are joint fifth in the all-time list.
Now the Three Lions must hope their talisman quickly overhauls those past greats as the scent of glory, absent for so long, is now in English nostrils, even if the path is barred not just by Italy, but potentially Germany as well.
Not that England strolled through.
The win had its sticky moments, not least the controversy that once again erupted over a ball that crossed the line unseen by officials.
Instead of starting on the front foot as Hodgson wanted, England found themselves penned back by a relentless tide of Ukraine attacks.
The general relief at Andriy Shevchenko's absence might not have been so obvious if the talents of Marko Devic were better known.
He was at the centre of most Ukraine attacks, had a strike blocked by Scott Parker and started a move that saw Andriy Yarmolenko step inside the box to force a low save out of Joe Hart.
Oleh Gusev shot over after being gifted possession by Ashley Young and late in the first half Yarmolenko slalomed towards the England goal only for Joleon Lescott to make a very late intervention.
Yet all the angst would have been removed had Rooney taken his golden opportunity.
For all Hodgson's assurances in recent days, it was evident that after just 37 minutes' action in 44 days Rooney was lacking sharpness.
The hoped for combination with Manchester United team-mate Danny Welbeck failed to click and his passing went astray too often.
That would have been forgiven if Rooney had turned Young's deep cross into the net.
It had been a brilliant move until final execution. Young, producing his most effective performance of the tournament to date, delivered the ball exactly where Rooney would have asked given he had intelligently peeled away from his marker. Level with the far post, the striker tried to glance it home and sent it bouncing wide.
In order to make the impact Hodgson hoped for, it was evident Rooney required a bit of assistance.
Three minutes after the restart Pyatov failed to clear a testing Gerrard cross and from roughly a yard, Rooney nodded in.
That raised England supporters' spirits and when big screens in the ground brought news of Sweden's goal in Kiev a few minutes later, the cheers went up once more.
They would have been silenced had the goal-line technology due to be voted on by FIFA next month already been installed.
But, just as Fabio Capello cursed Frank Lampard's goal not being awarded against Germany in South Africa two years ago, so Ukraine now have reason to lament.
To the naked eye, in real time, the officials saw John Terry hack Devic's half-blocked shot away but the slow motion footage showed the ball crossed the line and only those in the stadium were in the dark as the wise decision was taken not to show it to them again.
Shevchenko was introduced for one last hurrah but it was Yevhen Konoplyanka who brought an excellent save out of Hart with a dipping long-range effort.
Welbeck and Rooney were replaced as the clock ran down, while Gerrard and Ashley Cole also picked up bookings but that did little to dampen the spirits. ENGLAND: Hart, Johnson, Cole, Terry, Lescott, Gerrard, Young, Milner (Walcott, 70), Parker, Rooney (Oxlade- Chamberlain, 87), Welbeck (Carroll, 82) . UKRAINE: Pyatov, Selin, Khacheridi, Rakitskiy, Tymoschuk, Garmash (Nazarenko, 78 ), Gusev, Yarmolenko, Konoplienka, Milevskiy (Butko, 77 ), Devic (Shevchenko, 70).
REFEREE: V Kassai (Hungary). ATTENDANCE: 51,504.
HOW THEY FINISHED - GROUP D PW D L F APts ENGLAND .......... 3 2 1 0 5 3 7 France .............. 3 1 1 1 3 3 4 Ukraine ............. 3 1 0 2 2 4 3 Sweden.............3 1 0 2 5 5 3 Blanc wont get the Bleus after loss FRANCE coach Laurent Blanc remains optimistic despite the surprise defeat to Sweden which left his side facing a European Championship quarter-final against Spain.
Les Bleus were beaten 2-0 by the already eliminated Scandinavians, allowing England - who beat co-hosts Ukraine 1-0 - to snatch top spot in Group D and earn a last-eight meeting with Italy on Sunday rather than the reigning world and European champions.
But Blanc said: "We are disappointed of course, we wanted a different result, but the most important thing is we qualified for the quarter-finals. Even though Sweden played well, they are going home.
"We need to stay optimistic, we didn't make things easy for ourselves.
"It is not the easiest thing to play Spain at the moment, we have to be rested and need a really good performance to beat them.
"But we are going to focus and are going to fight. Today will be more optimistic than last night and I hope by Saturday we will be at a higher level."
Reflecting on last night's match, when goals from Zlatan Ibrahimovic and Sebastian Larsson condemned his side to defeat, Blanc said: "We were weak in certain areas of the pitch, too weak in the tackle.
"Sweden put everything into the game, they were better prepared physically and they have a player in Ibrahimovic who can make the difference . "I don't think we struggled going forward, we struggled at the back and in midfield. Sweden had a big physical impact. We hoped in the second half their intensity would drop but that wasn't the case. We conceded a lot of space but we also created a lot of chances."
GOAL: Wayne Rooney heads home to seal England's Euro 2012 progress in Dontesk