The disputed play will likely add to the pressure on UEFA President Michel Platini to reverse his opposition to goal-line technology.
"I was sad because the ball was in the goal by one meter," Ukraine coach Oleg Blokhin said.
Rooney, who sat out his team's first two matches at Euro 2012, returned from suspension Tuesday and headed in the goal in the 48th.
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.
It was Rooney's first goal at a major tournament since scoring four at Euro 2004 as an 18-year-old kid. He failed to find the net at both the 2006 and 2010 World Cups.
With the victory, England won Group D and will next face Italy in Kiev on Sunday. France also advanced, despite losing to Sweden 2-0 in the other group match. Ukraine, however, will have to watch the rest of the tournament as spectators, just like co-host Poland.
Ukraine had never won at the Donbass Arena on four previous occasions, and failed to seize on its advantage when it mattered most.
With their fans dominating the crowd, the Ukrainians were in control from the outset, far more confident on the ball and containing England inside its own half, even with captain Andriy Shevchenko on the bench at the start due to a left knee injury.
But early efforts were from distance, with Denys Garmash and Yaroslav Rakitskiy striking over, while England midfielder Scott Parker had to throw his body into the path of Devic's low shot.
They were getting closer, though, and looking more even menacing going forward with Oleh Gusev getting into the penalty area and sending in a shot that just creep over Joe Hart's goal.
Before Rooney scored, England came close to testing Pyatov when Ashley Young sent in a low cross that was easily dealt with in the 11th minute.
As Ukraine attacked the England goal, Rooney was quiet in the first half of his first competitive match in more than a month until he sent a free header wide in the 28th from Young's cross.
Sweden 2, France 0 • At Kiev, Ukraine, France backed into the quarterfinals of the European Championship, losing to Sweden but going through thanks to England's win over Ukraine.
Zlatan Ibrahimovic scored one of the best goals of the tournament with an acrobatic volley in the 54th minute and Sebastian Larsson added an injury-time goal to give already eliminated Sweden its first points of the tournament.
The margin of victory could have been bigger as France was outplayed for much of the game despite only needing a draw to guarantee a spot in the next round and facing a team with nothing to play for but pride.
The loss ended France's 23-game unbeaten streak but it still finished second in Group D after England beat Ukraine 1-0 in Donetsk. France will face Spain in the quarterfinals but will need a much better performance to give the defending champions much of a challenge.
England finished with seven points, while France had four and Ukraine and Sweden bowed out with three each.
France looked lackluster throughout much of the game and couldn't finish when it did threaten the Swedish goal.
Substitute Jeremy Menez had France's best chance to tie it when he broke into the area in the 81st minute but his low shot was stopped by goalkeeper Andreas Isaksson's leg. From the resulting corner, Olivier Giroud headed just wide.
Karim Benzema was largely ineffective again and remained scoreless at the tournament.
Instead, it was Ibrahimovic who stole the show with another spectacular goal to add to his resume. The tall AC Milan striker met Sebastian Larsson's cross from the left and put himself nearly sideways in the air before striking the ball perfectly past a helpless Hugo Lloris in the France goal.
Lloris then single-handedly kept France in the game over the next few minutes as Sweden kept pressing, making point-blank saves to deny Christian Wilhelmsson and Olof Mellberg.
Larsson finally added the second by emphatically volleying a rebound into an empty net and finally giving the large contingent of Swedish fans a reason to celebrate.
For France, though, it's back to the drawing board after a performance that would probably not go far against Spain.
P Quarterfinals: Czech Republic vs. Portugal, Thursday, 12:45 p.m.
TV • ESPN