Most of the headlines focus on making puns about the England striker's hair transplant - a spirit we've gotten into with our headline to this very piece - though as his post-match interview made clear, the Manchester United star pointed to his head after scoring to thank Andy Carroll for the loan of some hair gel, not just because his hair was surgically enhanced by Harley Street specialists last year.
Anyway, best of the hair headlines by far is the Daily Mail's "Thatch the way to do it", with a sub-head reading, "Weave got Italy next, thanks to Rooney (and a useless official)."
The Sun goes with "Weave done it", the Daily Mirror has "Hair weave go!" and the Daily Star has the bald but bold "Hairoo"... but the Daily Express's sub-editors missed the empty net with their "It had to be Roo".
As that Daily Mail sub-headline suggests, the main sentiment once you get past the Rooney gags is a sense of relief at England having beaten Ukraine to top the group. If you're north of the border, that relief is a sense of dismay, however, with the Daily Record going crazy about Ukraine's disallowed goal with their "Rooney 1 Looney 0.... Should have gone to Specsavers" headline.
The Independent's back page offers the best single-take snapshot of the game: "England get over the line" is the headline, with a stunning photo capturing the moment that John Terry didn't quite clear the ball off the line.
Inside the Independent, James Lawton offers an interesting, if bizarre take on how England made it through the group stage: "Lucky devil Hodgson must have done a deal with fate: He escaped what should always be known as the siege of Donetsk." The piece goes on to praise the "sensational" Ukraine side in terms so ridiculously generous that we genuinely wondered if perhaps Lawton had turned up at the wrong match on Tuesday night. Regardless, he admits admiration for the achievements of the England boss in getting his men this far: "After this, you wouldn't put much anything past the extraordinary momentum – and maybe the strange alchemy – of Roy Hodgson's regime. One that might – who knows – be in the process of breaking all the rules."
Tony Cascarino in The Times strikes a similar note of optimism after declaring Hodgson's pragmatic approach a success: "England's fans may not like it, they may not enjoy it, but the events of this season cannot have left anyone in any doubt as to whether Roy Hodgson's team can win the European Championship defending deep, playing cautiously and inviting pressure from their opponents...
"Can they beat Italy? Of course. And Germany, in the semi-finals? Again, yes. Can they win the competition? If Terry and Lescott stay strong, if their opponents continue to spurn chances, if good fortune smiles on them, they can. But it won't be pretty to watch."
In the Daily Telegraph Alan Hansen believes that the defensive approach will be found out any time now: "Spirit and endeavour can only take you so far. And while they have ridden their luck for lengthy spells against France, Sweden and Ukraine, with England struggling to keep the ball for periods of 20-25 minutes, the reality is that better sides will punish them if the same happens again in the knockout stages."
The Sun's Steven Howard also worries about the Three Lions' run of luck running out: "It was nothing to do with tactics, team selection and the use of substitutes. That England are into the European Championship quarter-finals is down to their luck holding."
Howard goes on to talk at length about the luck of the goal-line official making a mistake, though bafflingly he completely ignores the fact that the Ukrainian who was denied, Marko Devic, was several yards offside when he started his run.
The Daily Star's Brian Woolnough is not so worried, and is happy to place his faith in a manager who clearly knows what he's doing - even if nobody else does: "It's a pity Roy Hodgson was not given the England job years ago. We'd be world champions now. Whatever he's got, it's working. How, no-one knows... It left the nation scratching its head and asking 'how did we do that?'. But who cares, England are through."
While several papers focus, predictable on Wayne Rooney: "he remains England's gladiator," says Paul Hayward in the Telegraph", while in the Guardian Richard Williams writes that "Rooney added authority to the attack," even if he also added a missed sitter and many other rusty moments of frustration. The Daily Mirror's Oliver Holt goes even further in with his hyperbole: "This time, the Big Man really is back."
But the Daily Mail's Martin Samuel points out that there is only one man in an England shirt who has been pulling all the strings: Steven Gerrard.
"Put simply, Gerrard has been quite brilliant here this summer. He has been the player we have been waiting for; the player we have only truly seen with this consistency in the red of Liverpool. Gerrard knows he has not always justified his stellar reputation for England. He appears almost inhibited at times, his pronouncements speaking of the love he feels playing for his country, his performances suggesting a man sometimes overwhelmed by expectation.
"Credit manager Roy Hodgson with this current transformation then. Given the role of captain and complete faith in his ability to play box-to-box central midfield with the necessary discipline, Gerrard has thrived. "
Over on the continent, France's L'Equipe laments that the French side squeaked into the last eight "par la petite porte", or through the back door as we'd say on these shores, and questioning whether the side's long unbeaten run actually means anything at this point. "With the exception of a few moves by (Franck) Ribery, France never did enough to hang on to first place in the group... Too often reactive rather than proactive - a conclusion already drawn after the games against Iceland and England - it was inevitable that Les Bleus would lose one day."
The French paper also claims that the goal-line official's error was "karma" repaying the side for Frank Lampard's disallowed effort at the World Cup two years ago, and praises Steven Gerrard lavishly for his "tremendous job", and sees England as real contenders in the tournament: "More than ever, the Three Lions have their teeth bared ahead of their explosive quarter-final against Italy on Sunday."
Italy's Gazzetta runs a piece talking about how England's coaches have learnt well from their Italian counterparts to earn a quarter-final against the Azzurri - ironic, considering that this England side is led by one of the few British men ever to coach in Serie A.
The paper is scathing about England's chances against Italy, saying that "doubts about the quality of this England team remain... The dead-ball deliveries of Gerrard, some one-on-one talent from Young, and little else. Not even the return of Rooney, who was poor apart from his goal, did much to improve the team's manoeuvres."
Germany's Bild gets its teeth into the goal-line controversy, claiming that the "scandal" of the disallowed goal "rescued England" - a line which totally forgets the fact that England would have topped their group even if the goal had stood.
And finally, spare a thought for Ukraine as they go out of their own tournament. As Kiev newspaper Obozrevatel puts it, "Ukraine lost, but with dignity and even with heads held high... We leave this tournament, because there are those who are stronger. Or luckier. But we can rely on the luck and strength of this team for the World Cup. Now, it's our new goal."