Rooney atoned for spurning a 28th-minute headed chance from Ashley Young's pinpoint cross by nodding in the winner three minutes into the second half. Steven Gerrard did superbly to hammer in a cross from the right but Andriy Pyatov was culpable in allowing it to drift to the far post, where the striker, back from a two-game ban, touched into an empty net.
The United star was unlucky not to earn a penalty when Andriy Yarmolenko yanked at his shirt following a breakaway and he also fired a free-kick into the side-netting and forced a save out of Pyatov with a header.
"I'm delighted with the win and to score," he told ITV afterwards. "Obviously it's great as I've not scored in a major tournament for a while so it was nice to do that and get the goal that effectively won us the game.
"I thought our fans were brilliant and we deserved the win. We know our qualities. We're difficult to beat and I don't think any team will fancy playing us.
"We're going well at the minute and we'll have a good rest - an extra day's rest is important for us and hopefully we'll be back fresh.
"The main thing was to get through the group so to finish top is great for us. Italy will be a difficult game, of course, but we have to be confident and believe in ourselves. You never know. We have a belief and a ready for the challenges ahead."
Danny Welbeck worked hard in attack with little reward before being substituted with eight minutes left while Rooney was given a breather in the