England, France through to Euro 2012 quarters
The Manchester United player, ineligible for England's first two Euro 2012 matches after a red card picked up in the qualifiers, had the easiest of headers at the back post after goalkeeper Andrei Pyatov spilled a Steven Gerrard cross.
Rooney's goal in the 48th minute in Donetsk, Ukraine, had been the highlight of a lacklustre match which England only needed to draw to qualify.
But it livened up when Marko Devic forced a save from Joe Hart in the 62nd minute that was cleared off the line by John Terry.
Television replays suggested the ball had crossed for a goal but Hungarian referee Viktor Kassai waved play on.
Football's world governing body FIFA is currently trialling two prototypes of goal-line technology after a number of high-profile incidents in which goals have been disallowed.
The president of European football's governing body UEFA, Michel Platini, said this week that having five officials, as is the case in the current tournament, would prevent such an issue - but the latest incident appeared to undermine that theory.
France needed only a draw against already-eliminated Sweden in Donetsk to advance from the group stages of a major competition for the first time since 2006 and exorcise the ghosts of a disastrous 2010 World Cup, when players went on strike.
But Sweden was in no mood to help Les Bleus, as they sought to salvage some pride after a 2-0 defeat to Ukraine and 3-2 loss to England.
Swedish striker Zlatan Ibrahimovic opened the scoring in the 54th minute, volleying in a spectacular right-foot volley from 12 yards out while Sebastian Larsson made it two minutes before time.
The results left England on seven points and France on four, with both Ukraine and Sweden on three.
England will play Italy in Kiev, while France will take on European and world champions Spain in Donetsk in the quarter-finals.
The other quarter-finals see the Czech Republic play Portugal in Warsaw and Germany against Greece in Gdansk, Poland.
Germany coach Joachim Loew and Greece's players all tried to play down the significance of their match, with the German chancellor a hate figure in Greece for her insistence to Athens of harsh cuts to offset a crippling debt crisis.
"Angela Merkel and the national team are on very good terms. We have reached an agreement where she doesn't interfere with my tactical instructions and, in return, I don't deal with her political agenda," said Loew.
"As far as we are concerned, we are approaching a normal football contest and that is the end of it."
Meanwhile, UEFA faced criticism for fining the Croatian Football Federation 80,000 euros ($100,000) after a section of fans racially abused Italy's Mario Balotelli during their Group C game in Poznan, Poland, on June 14.
A stiff penalty had been expected after Russia was threatened with a six-point deduction from their Euro 2016 qualifying campaign for further serious crowd trouble and because of UEFA's repeated insistence of "zero tolerance" on racism.
But many people highlighted the harsher punishment meted out to Denmark's Nicklas Bendtner, who on Monday was slapped with a one-match suspension and a massive fine for displaying sponsored underpants during a goal celebration.
Manchester City and Belgium captain Vincent Kompany wrote: "Racist chants 80k fine. Commercial stunt 100k fine + 1 match ban... UEFA might need to review their order of priorities, don't you think?"
He added: "Surely if you were a sponsor, you would consider racism as a more dangerous association than the (damage) caused by commercial opportunism?"
Originally published as England, France through to quarters
