Sweden shocked France 2-0 in the other Group D game and as a result England, as group winners, will play Italy in Kiev on Sunday, while France, as runners-up will now meet Spain on Saturday.
Ukraine appeared to have evened the score in the 62nd minute when Marko Devic’s looping shot crossed the line before it was hooked clear by John Terry. But the goal was missed by the referee and his extra assistant behind the goal.
The disputed play will likely add to the pressure on UEFA President Michel Platini to reverse his opposition to goal-line technology.
Ukraine dominated the first half without really threatening Joe Hart in the England goal. And England made Ukraine pay for not converting their pressure into chances just three minutes into the second hald when Steven Gerrard whipped a dangerous cross into the penalty area that went past two defenders before Pyatov let it slip through his hands as he crouched to collect the ball. Rooney was at the far post and put England ahead.
France qualified for the knockout stages of a major finals for the first time in six years here on Tuesday despite losing their final Euro 2012 Group D match 2-0 to already eliminated Sweden.
A brilliant bicycle kick by Sweden’s inspirational captain Zlatan Ibrahimovic in the 54th minute gave them the lead with the outstanding Sebastian Larsson adding a second in the final minute of normal time.
It handed the Swedes not only their first points of the group stage but also their first win over France in almost 43 years dating back to October 1969.
The French, who also saw their 23-match unbeaten run ended, progress in second place in the group after England beat co-hosts Ukraine 1-0 in the other game to finish top.
France, who last reached the knockout stages of a major finals in the 2006 World Cup, will play champions Spain in the last eight.